Speed of hair growth based on weight?

Is there any truth to the claim that longer (and thus heavier, if worn certain ways) hair causes the hair follicles to produce hair at a different rate? That is, will longer hair will grow faster than shorter hair. Or hair pulled taught will grow faster than if it is let loose.

It seems like it could possibly make a small difference, but a negligible one. Maybe it was reported somewhere and grew into an old wives’ tale?

. . . or cause it to fall out.

Various means of stimulating the scalp are supposed to make hair grow faster than doing nothing. But I don’t recall anything about this being a major increase in the rate of hair growth. The weight of hair or pulling on it may have some minimal effect. And pulling too hard would cause an abrupt change in the growth rate.