Elhokar can be forceful if he chooses to be. We see him changing to be more forceful with Dalinar when he chooses to take his expedition. Blushweaver would find him interesting, as I believe part of the reason she was attracted to Lightsong was the fact that he wasn’t great at politics at the beginning, yet had to learn fast. Elhokar would certainly be attracted to Blushweaver because of her ambition and form, as she is a beautiful woman. If Blushweaver had to leave the Court of the Gods, I do believe that Elhokar would use all the researchers he has at his disposal to find a way to keep her alive and eventually discover that he can use Stormlight to help her. Blushweaver would certainly be a great match for the Alethi court, and she could help guide Elhokar through it until he learns his way. He wouldn’t be content with his wife leading everything, as it isn’t the Alethi way, so he would try to learn his way around politics by watching her. I believe Blushweaver finds change interesting and attracting, and Elhokar would certainly be in the process of change.
Let's go @Karger! Sorry I wasn’t on yesterday. Storms, I love debating.