I only go when I intend to fill it up.

It would be true (other factors aside), that less gas equals less weight, but it's pretty negligible per everyday usage.

 

I always fill up in all of my cars and motorcycles. Technically, and if you want to nitpick, you get better fuel economy by always keeping your tank pretty low, because gas has weight and lugging around extra weight in your vehicle wastes more fuel. Of course, if you have to go AT ALL out of the way to get to a gas station to fill up(even if it's only 1 mile out of the way), you're pissing away any savings that you would have made through keeping the tank low at all times by driving extra miles to get to the station more often instead of just filling up all the way and stopping for gas less often.

I also feel like it's a little better to fill up the entire way when adding gas too, because when you fill up, you're stirring up the contents of the tank. If I fill a low tank that only has 2 gallons of gas in it with 5 new gallons, that stirred up junk at the bottom of the tank is going to be mixed in with only about a total of 7 gallons of gas in my tank, instead of being dispersed throughout 20.5 gallons(a full tank)... so that junk is more likely to get sucked into my fuel filter before it gets a chance to settle back to the bottom of the tank in a small, low-tank, fill-up situation.