An insult for an ugly person whom you don't like, especially if they have beedy, untrustworthy eyes. Helpful if one is staring at you or your girlfriend, you are drunk and want a fight.

Internet persona(s) who happens to follow you and you happen to follow them back and maintain communication with and have a mutual liking for eachother whether it be friendship wise, etc. (Mutuals if more than one mutual)

Used as an insult of a similar nature to numpty. Twateye is not related to Cockeye.