In 5e RAW, a character with 20+ STR could carry one 300-lb barrel so long as they have nothing else worn or in their inventory. They'd be naked. (Carrying capacity is 15 x STR.)
A character with 10+ STR could drag a 300-lb barrel around, but not lift it. (Pushing/dragging capacity is 30 x STR.) I would argue that this would make it (nearly) impossible to position that barrel stealthily.
Just to be clear, I don't think there's ANY need here to become particularly pedantic about the EXACT amount kg/lbs a character should be able to carry.
The general point is: incredibly heavy items shouldn't be trivial to throw around on the battlefield. What's even more relevant, sticking to common sense here wouldn't be a case of "realism hampering game design" but actually supporting it, by giving a very legitimate reason to CONTAIN a potential recurring exploit.
Oh yeah, I don't think we need to stick to these exact numbers or anything, but since I saw someone talking about them upthread (with some mistakes), I figured I'd drop the actual RAW in as a starting point for discussion. The point was, unless we are making a large departure from the 5e rules and/or making barrels substantially lighter than they seem like they should be, moving barrels around should be incredibly difficult and doing it without anyone noticing should be even more so.