I'm a little under 220lbs, and I still struggle with being able to do more than 7 full range pullups, even though I'm very strong on pulldowns, rows, etc. The strongest I ever got on pullups was when I did about a month and a half of super-slow (10 seconds positive, 10 seconds negative) chins on the assisted chin machine. After that my regular non assisted pullup reps went up about 50%.