Contrary to logic, you might even want to use less than max pressure if you're a heavier rider. Your weight will compress the tire and raise the pressure on its own a little anyway. The bulge in the tire is a fact of life, unless you get a super high pressure tire or weigh 120 (like I did when I was in high school). I would try 110 as mentioned above and see how that feels as well, then choose what feels best, but not going over the max.
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It's like riding a bicycle