These are not SK rules, they are US DOT rules applicable to itineraries to/from the US. Forget the whole MSC silliness.

Whatever the allowance is for the first segment, that allowance will apply throughout the itinerary. Presuming that OP is on a single ticket CPH-IAD-PHX-XXX-CPH, his CPH-IAD allowance will apply thoughout.

Note that if IAD-PHX is a connection, not a stopover, OP's bags will be checked to PHX, but he will retrieve them for CBP at IAD and then drop them. If he is stopping over at IAD, he will collect his bags and then check them in with UA when he departs IAD and pay the third bag fee to UA.