Awwww... what the heck, let's get the calculator.

So, PLA has a densitiy, IIRC, of 1.2 grams per cubic centimeter. I have 1.75mm filament loaded up on my printer, I opened a GCode on Pronterface and it tells me it's 7221mm long.

So, first to get the weight of filament per centimeter (10mm), good all cylinder volume formula Pi*radius squared * height.

First the radius: 0.175 / 2 = 0.0875^2 = 0.07675, let's make that 0.0077

3.14 * 0.0077 * 1 = 0.021 cubic cm per cm of filament. At 1.2gm/cm^3 that's: 1.2 * 0.021 = 0.0252. So 0.0252 grams per cm.

722.1 cm * 0.0252 = 18.2 grams total for the object.

I just weighted the actual print and it was 22 grams, but it's been painted so it doesn't look to be too far off.