could changing grip, change the head weight?

Changing to a different weight grip WILL change the swing weight (not the head weight) but that's not as likely to affect performance as much as changing the grip size!

I've always preferred fatter grips, annoyingly just under mid-size, though they work Ok. Same with bats, sticks and racquets!

The 2 right 3 left (or similar) was a classic adjustment (along with 0.25 longer) that some fitters used to show they'd individually customised clubs! A 24 stone, tattoo-ed, pill-addicted (allegedly), Nigerian skinhead, to whom you just answered 'Yes Sami' when he told you his recommendation, was renowned for that (excellent fitter though)!