They are more than a bit of a mess. Nothing prevents either or both carrier(s) from charging. The only matter covered would be the actual baggage allowance. As a single itinerary terminating in the USA, whatever the first segment allowance was, carries over to the onward DL segments.

But, when it gets to excess baggage (as to #'s, weight, odd items), the rules are silent so each carrier can charge whatever it's tariff specifies.

That said, you can try filing an inline complaint with DL. They are at least responsive, but you really don't have a beef under their tariff and they will likely so respond.