I run my G603 on a single AAA battery with an AAA to AA adapter. So far I've been exclusively using "dead" batteries from other devices – each lasts a couple weeks! (In low Hz mode at least.. I don't feel any benefit from 1000Hz mode, even in Counter-Strike.)

Really depends on the on the mouse implementation: g pro is only 80g. It’s hard to get a wired mouse much lighter without a honeycomb shell (mice in that style can push into the 50s).