This is one of my pet peeves. Some people who are very close to me do this, and it secretly annoys me to no end. It might sound odd to complain about such a positive trait, but let's be honest here.
For example, if you aren't feeling well or aren't in the most talkative of moods, this person will ask "Are you okay?" When you say that you're fine, the person repeats the question and tries to pry any information possible regarding your current state.
While I appreciate the concern, in the end, what good does it do to ask? If I have the flu and feel horrible, no matter how many times you say you are sorry I feel bad, or ask what you can do to make me feel better, or ask if I need anything, it won't help. If I'm sick or depressed or feeling down, I usually like to sit quietly and deal with things on my own. If I need help in some way, shape, or form, I will ask for it.
I would assume that this is somewhat of an FJ thing, for obvious reasons. Not to put anyone down.
It's interesting, but if a T does something nice for me, it sometimes feels more genuine than if an F does it. If a T logically thinks through things and figures that I might benefit from something, I think that's a big deal. Don't get me wrong, many Fs are very good, heartfelt people. But sometimes it seems like they are acting on impulses that they can't help. Sure, they're just trying to be nice, but that's sometimes all they can think about. When someone who isn't driven by emotions does something nice for me there's an element of sincerity in it (of course, sometimes the T is just doing it because he or she realizes it's beneficial in the long run for himself ).