The main reason for heavy rubber mat is to damp oscillations of the platter (which is normally metal and would ring like a bell otherwise). Not really needed for a wood or fibreboard platter which are much less resonant.
Anti-static isn't much use in a mat unless the vinyl itself is conductive - typically the side being played picks up a lot of static from the stylus friction and the only decent cure for that is a little trailing carbon-fibre brush dangling from the tone arm, or some anti-static coating/spray for the disc itself. Static only builds up on the surfaces of insulators, and it causes two problems: audible clicks/fizz when sparks/corona discharge jump between vinyl and the stylus cantilever, and secondly it attracts dust like crazy.
Still a conductive mat will take off a lot of the charge from the side once you flip the disc over - can't be a bad thing, probably helps dust drop off again.
And heavy rubber lies flat, which is important.