Well, why don't you weigh your hair then? I weigh mine by leaning my head near a kitchen scale (the kind that just do oz/g) and letting my hair lay on the balance. You could compare wet vs. dry weight, as well. Also, compare the weight of your hair to the weight of everything else on your bike and your person.

For cycling, I'm much less anal about weight. But.. backpacking! That's when my inner gram weenie comes out to play. I have a backpack inventory with every piece of gear weighed on my kitchen scale down to the ounce. Then, when I'm looking for something to reduce or eliminate, I know where the big pig items are at. Other people I know just randomly chuck stuff out of their backpack until the weight feels right, but they're often eliminating the wrong gear.

Anyways, if it's really about the gram weenie thing then do the measurements and see how it fits into the big picture. But, maybe it's not about that. I kinda get the impression that you're interested in chopping your hair off and enjoying a daringly short haircut, but you're looking for the justification to take the plunge. I say go do what you want, who cares if it only saves you a few dozen grams? It's just hair, and it'll grow back!