People who pronounce the word "height" as if it rhymed with the word "width" are what I like to call faceburners. You know the type, they're so annoying and or awkward you can't actually look directly at them without squinting.
A woman I used to work with, I think her name was Ellen, made up a word, "fontrom," which suits my reaction to hearing "heidth." Fontrum is the shame-transference phenomenon that occurs when you see another person do something so embarrassing that you yourself become embarrassed. I experience fontrum every time I hear someone say "heidth." I think I find it so particularly poignant because it's one of those times when, by trying to sound more intelligent, the speaker betrays his or her native ignorance. Kind of like people who default to "I" over "me"--between you and I--in every situation, thinking that that's how educated people talk.