How can a 12 year old get big biceps and triceps without heavy weights?

Large biceps require both proper genetics as well as proper strength training. While any given individual may or may not have the genetic potential for large biceps, everyone has the genetic potential to get stronger biceps. Biceps are actually a relatively small muscle group. If you do a whole body routine or an upper-body routine, it's important not to overwork them--and overworking them is easy to do.

Ensure that you warm-up properly. Any exercise that pulls the forearm towards the upper arm will work the biceps. This includes all the variations of the curl such as standing dumbbell curl, standing barbell curl, dumbbell curl on incline, seated dumbbell curl, lying dumbbell curl and concentration curls. It also includes many exercises that work the upper back such as lat pulldowns.

Remember that, if you want to increase the size of your upper arms, it's more important to train your triceps than your biceps. The way it's usually thought of is that the triceps account for 2/3rds of the mass of the upper arm while the biceps account for only 1/3rd of its mass.

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