My Friend Always Likes Her Own Posts on Facebook

A topic came up on our radio show today. This, from a listener...

One of my Facebook friends is an older family friend, and I didn't want to accept her request . . . but it would have been awkward if I hadn't.

And now she comments on ALL of my Facebook posts.  She also always "likes" her own comments.  It's weird.

My friends have actually started giving me a hard time about it.  Would it be weird for me to unfriend her?  What do you do about an annoying Facebook friend?

Richard, 34

(This brings up a great question: Why would you 'like' your own post on Facebook? Perhaps they really don't know Facebook etiquette? What other strange things do people do on Facebook?)