1 gallon of water is usually a bit heavier in weight than a gallon of milk.
Milk also has different densities than water so whole milk may weigh a bit more than skim or light milk for example.
A gallon of milk weighs in at around 8.6 lbs while a gallon of water will weight in around 8.36 to 8.40 lbs depending on the room temperature where the gallon of water is stored.
The room temperature or outside temperature can also change the density of the water making it a bit heavier or lighter.
But water does weigh more per gallon than milk does.