The PSI in the tire is only one part of the story. The other part is how stiff (or not) the tire casing is. What you really need to do is (with help of a friend) measure tire DROP when you sit on the bike in the same position you ride.

So you measure from each axle to the ground unloaded, then get on and measure again. The difference between these two measurements is how much the bike dropped from the tires being squished. Next, measure the HEIGHT of the tire from the rim to the outer edge, do NOT use the width, and especially do NOT use the listed width on the side of the tire.

Let's say you're riding 700c x35mm tires with a rim edge to outer edge height of 37mm, and when you sit on the bike it drops by 5mm, that would be about 13.5% drop, which is just about perfect. Any less and you're riding an unnecessarily hard tire and would be better off letting a bit of air out, any more and you run the risk of pinch-flats and rolling resistance increases for no good reason.

Now let's say you get on the bike and measure 12mm of drop, that'd be 32.4% drop, which is much more than needed for an optimum ride. In this case you should inflate the tires more until about 15% drop is attained (different tires ride better/faster at different drop, so this is a rough, but fairly accurate figure).

If your tires are already at maximum pressure and your tire drop is still very much more than 15%, get wider tires, they have less drop at any given PSI and handle load better. For instance, 50mm wide tires would be easily inflatable to 50-65 PSI depending on model, and at that pressure, even at your weight they'd have very little drop, probably about 10% or less.