As with a lot of questions on here, the answer is... it depends.
In your particular case, you want to put on weight (hypertrophy) which is typically seen as lying in the 6 - 12 rep range (yes, it will probably vary person to person, but that's a pretty good starting point).
Without getting overly complex, I would recommend increasing the reps until you can do 12 strict reps (note: strict reps, so if you're doing curls, as per your question, these are not curls where you use your whole body to give the weight momentum allowing you to curl it, just use your arm(s) to curl it), then upping the weight and dropping back down to 6 reps, then start adding reps again until you hit 12, increase weight, drop reps, so on and so forth.
This will give you a simple progression to follow as you get stronger and more experienced.
That should help with your specific question.
Now, taking a slight aside, if you haven't already, I would recommend finding and running with a program from an established strength coach, with an eye to hypertrophy. There are several out there, from books or blogs, that should do the job. Getting a program like this should also give you some idea how to progress, sometimes it's weight, sometimes it's reps, sometimes sets and sometimes more advanced variations of the exercise.
Alwyn Cosgrove and Lou Schuler's New Rules of Lifting for Women I've heard good things about, and I believe Bret Contreras' Strong Curves program is well regarded (it also has from what I gather a pretty supportive Reddit sub).
A program like this from a well established author should also run into arguably the most important aspect of putting on weight, diet.
If you can afford it, you may also want to consider hiring a good personal trainer, or looking at group training sessions (I train in a group with a girl who failed the UK Navy fitness test on the grounds of being grossly underweight. Through training with the group, as well as the support she gets from everyone, she's put on a good amount of healthy weight and is a lot happier).
Hope some of that helps, good luck with your journey!