This is all on one ticket? What kind of plane are you on from PDX to SFO? And when are you flying? If this month, you could have a problem with delays at SFO.
Knowing those answers will help people give a good response. My initial inclination was to say carry it to SFO your self and check it there, thinking that is one less transfer to go wrong. But I don't know what the connection procedure is at SFO. I am thinking there is no way to transfer between your flights (domestic to international) airside at SFO, but maybe I am wrong.
As i see it, you will most likely land at T3 where the Alaska planes land (on domestic routes, not Mexico). Then you will use the Airtrain Red or Blue Line to get to the International Terminal for your BA flight to London. If you are checking the bag there, you will have to go through the baggage check line at the BA desk along with all the passengers who are starting their journey at SFO. But most of them should already have gone through the line. So the question is how long will this take and whether it would slow you down significantly. You still have to go through security.
So after thinking this through, I am leaning strongly toward checking it the whole way through. We have never had a problem with bags checked with Alaska, and for flights to Europe on BA (our usual airline) we have only had a bag go missing once. That was our daughter's bag when she flew from SFO to Rome. The bag did catch up with her 2 days later. Whether this glitch suggests there may b problem with baggage handling at SFO I have no idea.
I will be interested in seeing what others have to say. ( And I will bet that someone will advise you just do carry-on the whole way).