Based on my assumption that while on rough surfaces: "If it feels smooth, it's probably fast too." I have settled on 25mm Michelin tires. But I don't get what you mean about thick?
The hoop stress in a tire casing increases with the tire's volume, so a fat tire must have a sturdier casing than a narrow tire if it is to have equal strength. Usually a fatter tire has thicker tread rubber than a narrower one, but this I believe is based on custom rather than on engineering principles.