To have a minimum, you have to have a set of constraints. There's no reason those constraints could not lead to "weak governments in all levels of government"

I must be misreading you. I keep finding people making these broad over generalizations about libertarianism. Yes, libertarians are for minimal government, but minimal is a term you can drive a truck through. Simply because one libertarian believes that limited government is minimal, tiered, distributed government and another thinks it means single-layer, centralized government doesn't make one person libertarian and another person not.

The terms you mention are not simplistic, they are broad. There's a big difference. It lets a lot of people have libertarian leanings and prompts the individual to continue the definition process at a personal level, which is exactly what you want in a democracy, right?