Yeah, it's a pretty versatile phrase that's hard to explain. But it does often have a connotation of childishness or naivety, even when used sincerely.

It is often used an expression of thanks or appreciation, but I associate that more with an elder speaking to someone younger.

Most of the time, it is an genuine expression of true empathy, but it's not uncommon to be used as a passive aggressive expression of false empathy. It's that childish connotation that give it the extra bite when used passive aggressively.

And that plausible deniability, where the phrase is used in a genuine context often enough that sometimes you can't tell that someone is throwing shade, is very much a reflection of southern culture.

Source: Grew up in Georgia and North Carolina, with some family in Alabama.