the fact that a certain amount of distance / weight / volume is technically infinitely divisible

Is it though? There's a minimum distance called the Planck length. It's literally impossible to resolve an object's position at a higher precision than this distance. Could you divide something into half Planck lengths? Maybe theoretically but I'm not sure what that means in reality.

Same with weight. What does it mean for something to "weigh less" than a neutrino? You can't cut a neutrino in half. So again, you're talking about theory rather than reality here.

Sure, we can "theoretically" try to come up with what it means for distances smaller than Planck lengths or masses smaller than neutrinos... but then you're again talking about infinity as a concept rather than actually existing in nature.