If the airlines have interline agreement in place, this allows for flights being booked on 1 ticket, and the baggage will be transferred among the airlines. Under US DOT regulations, the first carrier's baggage rules apply, so for your outbound you may be assessed $30 for the first checked bag. Check in with Alaska, and the bag will be tagged to your destination.

You will need to check in at SFO, or at the transfer desk if you are making another connection outside of the US, for the remaining segments. It's also a good idea to present your baggage tag at that point so they can add that information to your PNR, and also to verify that they received the checked bag from the other carrier.