To say bless someone’s heart is an insult or a way of making fun of people in Mississippi. The informant said if someone were to say it about them, they would think the person didn’t like them. It’s a way to be fake nice and to curse someone out without actually cursing.
I think that this saying is very similar to euphemisms and an example of tabooistic vocabulary, but rather than replacing a specific phrase it replaces a multitude of phrases by just conveying the intent of the message and the impact the message is meant to have on the listener without having to use a specific example of the misfortune or dislike felt towards or wished upon the subject of the heart-blessing. The fact that the community is Christian is probably a large factor in why this way of insulting people became popular. Since it is looked down upon on a spiritual level to be rude, and especially to curse people, they have acclimated to using words that are kind and well-wishing in an insincere way for expressing their negative emotions towards each other.