How do i increase the weight i lift?

Recently i've been working at builing my arm muscles and i've been lifting 2kg free weights. I now feel that these are too light but the next weight up (3kg) is too heavy (I tried it today and i could hardly do half what i normal do routine wise)

There isn't an in-between weight and i was wondering what i should do. Do i continue with the 3kg as i will get stronger and it will get easier or do i do half with the 3kg and half with the 2kg weight?

@Lie - Awesome. If you couldn't guess I am fairly new to weight lifting so i'm still a little unsure about some stuff but your advice was really clear and helpful.Thank you

I've gone from 10lbs to 25lbs dumbbells in a week! Repetition is key. Lift often, whether it's everyday or every few days. When you lift, lift one arm first, then when you go down, go down slow. You'll notice it's harder to go down slow because your muscles are fighting gravity! Then do the next arm.Remember to use proper technique. Keep your arms straight and lift only the section of the arm after the elbow. Don't dig your elbows into the side of your body or that's cheating! . Do enough reps until you can't do anymore. And I mean CAN'T. Like when you try to lift but your arm is just failing because it's so stressed. Take a little break until you can lift again (1-10 minutes) then lift as much as you can again. If you literally can't, do it again THE NEXT DAY. (Btw your arms WILL be sore) That's what I did when I lifted 10lbs, and I could only do like 8 or 9 reps per arm. The next day, I could do 15 reps per arm. Then I moved on to 15lbs the day after that, and could only do 6 reps. If 8 reps is your max, that's how many lbs you can lift. So right now, I can lift 25lbs 8 times per arm and that's my max. 25lbs is what I can lift.Consistency and persistence is key.

I'm assuming you're a girl or you're really young because 3 lbs is incredibly light even back when I was in middle school. Well how many reps do you do with the 2lbs? Also I'm assuming you're doing bicep curls? I think key to moving up in weight is to do less reps. Basically warm up and try to do like 3 reps on a heavy weight. Obviously if you're able to do like 3 sets with 8-12 reps it means that what you're lifting is too light.
When you're only able to do like 3 reps that's when you know you're pushing yourself to the limit. Well that's what I do anyways and now my warm ups use to be my limits. Setting new prs with practice, motivation, drive, and focus. But you know you could do whatever you want if you want to do 1 set and 50 reps that's up to you. 

3lbs?? how do you carry your grocery bag from the store to your home? or carry your back pack to school?
if you are talking about doing as many reps, don't, just move up to 5 or 10 lbs and do less, even if it means a lot less, once you cant, move down weight. 
just for me, increasing reps increases strength, for example when I couldn't curl 40lbs, but could do 25lbs 10 times without too much strain, i increased it to 20 times/rep, then then went up to 35lbs and could fairly easily do it 10 times. later i realized i could curl 45lbs, but felt it was somewhat unnecessary to put additional time or effort into curls... as the biceps are pretty small muscles and are rarely used compared to your other muscles such as your core, back,  and quads. or ever your chest.
better to do push ups, pull ups, squats, calf raises, and extended horse stance since it surprisingly works different muscles than regular squats. 
and assuming you area girl since ur lifting 3lbs, working on your bigger muscles, like your butt and thighs, will cause more consumption of calories while resting which will lead to more weight loss compared if you just worked on your arms, even if you do less effort on other parts of your body, you will build up more overall msucle mass or density, and thus burn more calories... 

lower weight with a high amount of rep aren't going to do you justice.

instead try to work on heavier weight and lower amount of rep
using heavier weights for 4-8 reps will build you strong muscle and that's the truth. also it's really important to look at time under pressure. slowing down the motion between the reps, flexing the whole way through, and focusing on keeping the weight controlled will help a lot. and also do compound lifts instead of single target lifts. otherwise they will eventually screw your body over.

To increase the lift you have to slowly work on it, in starting lift little weight then slowly you start lifting the weight to build muscles. One more way is you have to increase the number of lifts or performed the same number of lifts repetition day by day. 

I didn't see anyone else mention it, but you should focus on negatives. i assume you're doing bicep curls? so if you can't lift the weight up, you should start on the top position and SLOWLY, in a controlled manner, bring it down. repeat.
as others said, keep reps low. 5 sounds about right, but no higher than 8.

Well, try to hire some professional trainer who will train you properly for lifting your weight process, they know the good tactics as well as suggest you the good process for lifting the weight slowly and according to step by step process.

Repetition is the key to this one. Keep doing the 2lbs with more reps per set. Lets say 20 lifts in 4 groups then slowly increase it.
Another method is to keep doing it until you cant lift it anymore.

Otherwise push yourself to do 3lbs and it will eventually get easier.

I lift 180lbs (and more) in bench press right now and I started from 90lbs c:
The reason why I could do this in a year was a huge amount of body weight training!
You should start with that first and then slowly go to dumbells c:

Since this topic has been revived I may as well take the chance to say what I think is very important for everyone to hear.
Used to be a personal trainer and I can't stress this enough - TECHNIQUE will always be the easiest 'shortcut' to lifting heavy and will also keep you from being injured. Have a professional show you the right way to do something. This goes for any sport of course.

I started powerlifting when I was 12 and my coach was a Junior World Champion Powerlifter back in his day (When he was 23). He had me start with a 'broomstick' since I was so young and it can be harmful to start lifting heavy straight away.

I'm now 18 years old, under 53 kg and deadlifting 120kg, benching 72.5kg. 3 out of the 7 people I trained had improved on their technique and within a week, they could 1 rep max at least 10kg more than usual. Usually this was for their bench since there's multiple details a lot of people miss out on regarding their technique for this. It's surprising how many people don't know to pull their feet in as close to the bench (until their heels are slightly off the ground - they'll come down when you take the bar), push with your heels, arch your back and the line of your bar should start at your chest and end above the base of your neck at the top of the lift. ALWAYS HAVE SPOTTERS when attempting your 1 rep max.

As for progressively training to lift heavy in the long term, try to build muscle by doing 4 sets of 8 reps (of whatever you can manage) and keep on track with your nutrition. This means meeting your macros, manage protein and hydration etc. Always let the muscle group you trained to rest for a day. Training your muscles tear/rip them so they need time to repair (with assistance of proteins) and become stronger, helping you to lift heavier. Being able to increase your lifts is the most amazing feeling, always challenge yourself and don't get hung up on comparing your lifts to others - You'll get there eventually and perhaps go even further! Happy lifting

Don't try to increase the weight suddenly slowly increase the weight you lift otherwise it will effect you or you can also suffer from injuries. 

Guys, thanks for all the replies. I'm now lifting 4kg (NOT lbs like i mistakenly said in the original post - which I have now changed!). To be this is a big deal, I've struggled with an eating disorder for 10 years so my muscle mass isn't what it should be and seeing myself get stronger is a huge confidence boost

I have taken everyones advice on board and I can see that I'm not trying hard enough. I'm not lifting until I can't lift any more but I will start doing this. I will also look at hiring a personal trainer when I move gyms in the new year (I use the uni gym right now and there isn't the option of hiring a PT)

I will try 5kg on Monday but lower number of reps

I would try lifting in multiple sets. Take a minute to two rest time in between your sets. Have fun~ :]