The amount of gasoline weight you are carrying around will affect your gas mileage in such miniscule increments, that it will be immeasurable. Your driving behavior is the biggest determining factor on gas mileage. If you drive more aggressively cause you think you're carrying less weight, it's going to erase any and all fuel economy by driving with an empty tank and saving 90lbs of weight.
Ultimately it's your car and this is America, so you can do what you want. By all means, if you really think this is fun or a good idea, have at it. Hopefully the stress you are putting on the fuel pump will manifest during the warranty period. If not, the money you save on gas can be used to replace the fuel pump.
Fuel Pump Tech
Everything you wanted to know about fuel pumps!
I was not suggesting that running down to empty is a good idea. I was simply stating that I didn't see any mention of fuel weight in any discussions. The difference between a full tank and empty is about 120lbs... about 3% of he total weight of the vehicle. Easily calculable in fact... a difference of about .75 mpg.