1) Does your significant other like Weird Al?
Yes! He's a casual fan.

2) How important is your S.O.'s opinion of Weird Al (or any other music/comedy taste, for that matter) to your relationship?
For me, good taste in music and a rockin' sense of humor are two of the MOST IMPORTANT qualities I look for in a significant other. My boyfriend has both of those. As for the Weird Al thing, I'd at least like my significant other to be able to tolerate my fandom and be respectful towards it, as it's a big part of my life. Luckily, my boyfriend not only respects it, but he even told me the other night that he thinks my Al fandom is adorable. So I'm happy about that. I told him I'd take him to a concert one of these days, and he got really excited. He's a HUGE Star Wars fan, so I think he'd really enjoy himself.
3) If they don't like Weird Al, what have you done about it?
Don't have to worry...he likes him!
4) Any other stories about current/past significant others and your relationship with them as it pertains to liking/disliking Weird Al.
Nothing terribly important. The other night I was at my bf's house and Al's Behind the Music came on at 11pm. I didn't know it was gonna be on, so when the program started, I got all hyper and excited...we're talking, like, rolling-around-on-the-floor excited. He totally got a kick out of my Al-thusiasm. I was about to go home at that point, but I decided to stay a bit longer so we could watch it together, haha. My mom understood, I think.