OP, what you need to be concerned with is the strength/stiffness of the rim, and number of spokes--you want a lot of them! Thicker heavier spokes actually have less stretch. Thinner butted spokes are usually stronger than thicker straight gauge spokes because of the working of the metal to produce them. I know that seems counter-intuitive but Sapim CX Rays (very thin) have the highest fatigue life of any spoke out there. You could have a very nice and dependable wheelset for your weight that has thin(ner) spokes if appropriate components were used and they had a quality build.

However, I realize that what you probably really wanted was an economical retrofit for your existing wheels, and what I'm telling you likely means that you need different ones. Sorry about that.

I had a coworker a few years back that was about your size. He had some 32 spoked Mavic Open Pro wheels that came with his bike that were very problematic. After fighting to keep them true for a year or two, he finally gave up and had a custom rear wheel built on a different rim to suit his needs. He was a happy high mileage camper after that. I maintain that the best every day wheels for most riders are the ones you rarely have to think about.

What wheels do you have? How many spokes?