"You used more hot water than I did so I should pay less for the utilities"

"I weigh less so I should pay less for the gas for the rental car"

"Mosquitoes don't bother me so I will not pay for 1/3 of the bug repellant"

I don't get it and there must be some other history going on here. Lactose intolerant? A gallon of Lactaid milk is a few dollars more than regular milk - can't believe a family fight over something so petty.

If fight is between you and your sister, I would divide by 4 and you pay 2 shares - it is worth what I would guess is maybe $10-20 for peace.

If argument is between either you or sister and Mom, suck it up and do the same.

This has the feel of some long-simmering feud that all the easy and equitable solutions in the world will not fix.

How about if everyone does their own grocery shopping, pays for and brings their own food?

Purchasing their own specialty items, plus some extra food items to share with others, and maybe ingredients for making a meal for everyone.