First of all, equating your weight in pounds to tire pressure in psi - and you certainly can't add the pressure in your tires and compare it to your weight.
If your weight is 225 lbs, that's over 100 lbs per wheel, and the link shows that for 100 lbs on a 25mm tire you should be running 110 psi - 120 for a 23mm tire. For ~112 lbs/wheel, your pressure should be more like 135 psi for both wheels if you're running 23's.
If you're going on the assumption that your rear wheel is loaded more heavily (say a 55/45 split), then you'd want something like 120 psi for the front (101 lbs load) and 148 psi (123 lbs load) for the rear. Which would suggest that you may want to step up from the 23's to 25's so you could run 110 front / 136 rear.