Also that it is not covered by any rule in the PHB which would allow it.
Two thigs:
1) As far as i know, rules in PHB explicitly encourage players to use their own imagination and fantasy to do litteraly anything, and use those rules as guidance ... not as restrictions. > That is your allowing.

2) As far as i know, there is no rule that would forbids it either.

And finally that its physically impossible to add a 300 LB / 130 KG Barrel to a backpack, let alone feasibly carry even one.
Show me such barrel in game, then we can talk about why is it possible.

BTW do you know what else is physically impossible?
To carry 25 chainmail armors ...
Or to carry 25 warhammers ..
Or to carry 25 greatswords ...
Or, funny enough, to carry all abowe, enough food for next three weeks, your own weight in gold, also carry your own armor and weapon, and still juping 7m long jumps.

How is that possible that none of that is problem sudently? :P