Feel free to work with other rep ranges than just sets of 12...
for example
3 sets of 8-12 reps
5 sets of 4-6 reps
8 sets of 3 reps.
All of these can be done with weights that will just about cause failure on the last rep of the set. When you use lower reps, you can use higher weight. This improves your neurvous system's ability to use your muscles efficiently. If your goal is size, but not necessarily strength, you should certainly try to keep the total number of reps you do close to the same no matter how many reps you do per set, which means doing more sets if you do low reps per set.
There is an inverse relationship between the load you are using (intensity) and the amount of work you should be doing (volume).
Experiment to see what works for you, but you certainly can use heavier weights than you are now, it just may mean doing fewer reps per set. That's okay.
Best wishes
PS - check out this article by Ian King:
High Intensity Versus High Volume