Pesky Characters and when to dump them

If you're a writer, or know a writer, you'll know that us writers hate to cut anything out. All that time spent on a gorgeously crafted scene? Every word, sentence and plot arc is a blood testament to my art. Right?
So, I've been nitpicking my last chapter over and over and over. Re-reading, editing, tightening... staring at the page for hours on end. I just couldn't seem to move on. The problem? There was this character, a delightful character with a walk-on role earlier in the book but with ...