Lift heavy? You will not get much hypertrophy near your 1RM. If lifting heavy got you bigger, then how could powerlifters increase their bench or dead between comps without changing weight classes? The fact is if you lift heavy doubles or triples like I do to cycle up for push-pulls you will not gain much size, say arm size. Powerlifters are not that big at all in proportion to their 1 rep max lifts. Hypertrophy is best achieved at 60-85% of your maximum with a lot more volume. I'm actually doing a hypertrophy cycle after months of westside. My bodyweight and measurements are changing weekly now, but I did not budge my weight at all while doing westside despite increasing my bench 22%. Most of the adaptations to maximum effort training are fiber transitions (ST - FT), neurological adaptations and form improvements.
So lifting very heavy, near your max will not make you big. It will make you strong. Working out 60-85% of your maxes at a high volume is the best way to increase muscle size.
That being said, I believe that going near 80% gives a thicker physique than the guys who coast around 60%. Franco, Lou, Ronnie, Dorian, etc prove this.
Let's take a bodybuilder who's one-rep max squat is 425lbs. This is a good beginner/low-intermediate squat number. That bodybuilder will get a lot more size doing light sets of 75% of his one-rep max (which means 4 sets of 10 at 315lbs (75%)) than he will going heavy at 95% (doing 2 sets of 2 at 405lbs). There just isn't enough volume for good growth stimulus going heavy (95%) as there is when going light (75%).
Anyone who wants to read about all the latest training theories and periodizations along these lines should check out Tudor Bompa's (the Romanian Olympic weight training coach and trainer of 11 medalists) book Serious Strength Training, the second edition. It has EMG studies of exercises, explanation of hypertrophy, mixed, and max effort/powerlifting phases to blend to your satisfaction and goals. Very interesting read, even if you ultimately discard it for yourself.