No, libra (the unit of mass), and libre (being free) have unrelated origins, afaik. Libra comes from scales, as in the Libra constellation, wheveas libre comes from liber, related to freedom (and not books (or “libro” in Spanish); that’s a different word), which apparently comes from even older languages, meaning “town” or “people”.

An inch is about a thumb’s width and if I remember my guitar lesson correctly, isn’t pulgadas similar to the word for thumb?