I was actually shocked that Alaska Airlines has not changed its first class baggage allowance to match American Airlines or most US major airlines.
70 pounds is the norm.

Anyway I was on a SEA-LAX-DCA flight two months ago on a paid first class ticket.
The agent noticed that my bag was 53 pounds and told me to move my stuffs or paid. I just chose to pay, as I would rather her doing additional paperwork than me trying to repack my bags in front of a busy first class check in queue.

In the end, Alaska Airlines somehow did not put my bag on the flight that I was on. I checked in three hours in advance for those who might think I checked in late.
They ended up retagging my bag on the nonstop SEA-DCA flight, which arrived an hour later than my LAX flight. I chose to wait at the airport because it was easier.
I wrote in a complaint and Alaska agreed to refund my overweight bag fee, since they failed to deliver my bag on the right flight.

The moral of the story is that Alaska Airlines is not flexible with the 50 pounds weight limit and those agents especially in Seattle will not budge under any circumstances.

Carfield