BAF, Lets have a little girl talk...
Just my two cents worth is that he is most likely married. I get this a lot from men who are not truly available. They cannot call you at normal times or meet up with you after work because they have these lengthy stories about their commitments. My usual response now is that it sounds like your life is too busy for a relationship/friendship and so you should find someone that accepts those terms.
He only calls in the morning? Unless he works nightshift that's a red flag. I've dated men who worked night shift before and they still found time to call me in the evening. The texting is suspicious too... he can do that when someone else is around. If he only calls in the morning and texts at night you've got your answer.
oooooooooo I agree with Mack and D and everyone who says PROCEED WITH CAUTION.
Big girls or not, dude sounds like a stalker-type to me. Those types always show their hand early but a lot of times women dont recognize it because it can seem very flattering (at first!)--he will be telling you that he doesnt understand how it happened, but somehow he has FALLEN IN LOVE with you in about two weeks (and will be serious wit' it)
PROCEED WITH CAUTION... and don't let him get you on ANY kind of schedule because if you call one minute late or whatever he will clock and show his true colors...
(Just my opinion, of course)
PB