line on water is bonded to the water via adhesion. (two unlike/not the same molecules bonding- pvc:water) the line is adhering to the water http://en.wikipedia.org/wiki/Adhesion
the water molecules themselves are bonded together via cohesion (two of same bonding together- water:water), this allows the line to float via the surface tension. if water is still bonded to your line during your cast, then yes, it will be heavier (until the velocity/force of the cast makes it falls off)
you have to pull the line away from this bond -breaking the bond. that tension might be what you are feeling as weight. this allows you to load your line on the water and reduce false casting. just pick it up and throw it in the direction you want.
same thing if you wear contact lenses, you have to break that bond from the lens to your eyeball that is held there by moisture.
casting on grass, the line just sits on the blades. you might feel tension form the microscopic silica in the grass that is catching the line when you pull the line off.
wet line weight compared to dry line weight reminds me of the term that someone skinny person is 110lbs wet when they look maybe 100lbs.
hope that make sense