I was just thinking about these words and was curious what they might be called. After a little scrounging around on Google, the best answer I could come up with was "reduplication." This doesn't seem to be the best fit though, as it focuses on meaning through the duplication, and not the duplication itself.
I was wondering, though these terms are generally used in endearing relationships such as with children or significant others, does anyone know if words like these follow a linguistic tendency/rule/etc., and does it have a better name?
