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.
2 Yonex VCore Tour G - Kimony TecniLeather grip / 320g unstrung - strings TBD