It's hard to come up with a single term without knowing the person in question because I would be generalizing. There may be different motivations behind such behavior: a cultural and regional habit, insecurity, courtesy, or a "I-don't-owe-you-anything" type of answer.
In the Western Civilization, If this specific person is always anxious to repay any kind of favor, big or small, and feels very guilty if they can't, that is surely pathological and I wouldn't call them "responsible" or "grateful". It is certainly a manifestation of a personality disorder. A "normal" adult might just say a warm "thank you" and not feel guilty. Of course it also depends on the favor itself. There are "favors" and there are "favors".