Go to 28's if your frame/wheels can handle it.
I had 23's when I started riding again earlier this year. I weighed 240ish then and pumped the tires up to 120. Felt like I was riding a box of rocks -- extremely harsh ride. Before long got a snake-bite flat, and decided to get smart.
Changed to 28's, and got smart about inflation; 90 in front, 105 in back.
HUGE improvement! Jolts that used to knock my teeth out are still healthy bumps, but not nearly so harsh.
My weight is down to under 200 now, and hopefully will continue to drop. But I'll keep the 28's.
-Tom in SoCal