Do you save more gas by filling up the tank as opposed to putting in a set dollar amount?

Do you save more gas by filling up the tank as opposed to putting in a set dollar amount?
Basically the heavier a vehicle is, the more power it needs to move and therefore has a larger consumption. This is why if you fill the tank full, the car will be a bit heavier and therefore will burn a little bit more. However the difference is really insignificant.If you want to ask more experienced environmentalists and hypermilers, join a gas saving community like http://www.gassavers.org Nik