Tournagrip is actually one of the best overgrips out there for heavy sweaters. It absorbs sweat as no other.
Overgrips can be divided into two main categories: the absorbent ones and the tacky ones. You need to find which one you need and the right overgrip that satisfies your needs.
For example, I need the most tacky and thin ones, so I'm using Gamma Dermagrip.
4 Head IG Radical MP - Pacific Poly Force Xtreme @ 47 / 332g / 7 pts HL / SW 325 / TK82S
Gamma X6-FC // Member of 18x20 club