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Sorry, you're out $10.

Codeshare/no-codeshare has nothing to do with it, with any airline. It's all the operating carrier of the first flight in that day's itinerary. If your "Continental" flight at your baggage-check airport is operated by JoJo's Flying Service, you follow JoJo's rules.

(Or United, or American's - yes you can have a non-codeshare flight issued on the same continental ticket on a competing non-partner airline).

It always follows the rules and fee structure of the airline with which you check the bags. The fact that 90% of the travel later that day, on which the bags are already checked, is an airline where by status or cc or cabin you would get free, doesn't matter.

Here's the one case when it does matter, usually - if your originating flight with JoJoAir/no-status/bag-fee airlines is on the same itinerary as an international (as in intercontinental) flight, in most cases you get the allowance of the international carrier. But not always.

It's just the way the system works. BTW, as a CO Silver you're a Star Alliance Silver, US should have waived your 1st 2 bag fees - that's US' policy (goes a bit beyond what *A requires for *S) - assuming this was after CO joined *A last November, and you were already a CO Silver.