When you start going to the gym you'll hear people talking about progressive overload. Simply put, this means that if you're hoping to gain muscle over time, you need to (1) train with enough intensity in order to overload your muscles and stimulate new growth, and (2) gradually increase the resistance over time by either adding more weight, increasing your number of reps, or taking shorter rest breaks between sets. Progressive overload is essential when it comes to building muscle. Recently I moved up to 25 pound dumbbells for my curls.
I can manage about 12 reps before my form suffers. I know that 25 pounds doesn't sound very heavy but it's the most I can do. Don't try to add weight too quickly, because the quality of your training will gradually decrease. You're also more likely to get injured, which means you're going to have to take time off to heal. The key here is progressive overload -- gradually and consistently over time.
Happy lifting!