Thicker spokes are not "stronger".
Well they would resist a great static tensile load, but that is not what breaks spokes on bicycles.
IF your hub is still in good condition and IF your rim is not worn on the brake track then it MIGHT be worth rebuilding with all new spokes.
Buy stainless steel double butted (2.0/1.8/2.0) with brass nipples.
Sapim Race
DT Swiss Competition
or if money is tight ACI Alpina
The thinner middle section is what makes them more resistant to fatigue failure - which is what breaks spokes on bicycles, but ONLY if they are tight enough. Don't rely on your LBS to get them tight enough. Do the truing and tensioning yourself.
This article is good for getting the tensions right if you don't have tensiometer. I used it for the first dozen or so wheels I built (including one pair for a real lard arse friend). No broken spokes on any of them.