I rode a set of 28 for the first several years after returning to cycling. I was new back to the sport, and with the "newly" acquired prosthesis, didn't want to take any chances with flats of any kind. I used a set of hard case tires, which I am sure had some impact on the feel, and turning was very slow and cumbersome feeling compared to the 23 that came on, and that I later switched back to.
With that said, I NEVER had a flat with those tires of any kind.

I am a 210~#, and have weighed considerably more. I swapped back to 23 Conti's, run them at about 100PSI and have had no out of the ordinary issues with them as far as tire or rim are concerned. If you aren't having issue now (but second the idea that you lower pressure some) then I don't suspect you have any real reason to change to a larger tire unless you just want to.