What difference between -- I appreciate / I do appreciate ?
As a native speaker, I would say that "I
do appreciate" normally carries a sense of contradictory emphasis. For example:
"I appreciate the the gift you've given me."
"I do appreciate the the thought, but I already I have one of these."
In the latter instance, the "do" serves to emphasise the main verb "appreciate", but the emphasis is added as a counter to the negative expression that follows. In my experience, this is the sort of context in which "do appreciate" is most often used.