Well, the problem may step from her being 16 and you being in your 30's. If her parent's do not approve of the relationship--------- she may not be comfortable accepting gifts from you. I think the best gift you can give her is to wait until she reaches 18 plus years of age to pursue a relationship with her.
maybe she has low self esteem and feels bad receiving gifts, how does she reac when others give her gifts? give her gifts someimes, to say thankyou, tel her you love her daily, and dont give her anything to extravigant. i dont think its about not giving her what she wants, but maybe that she already has what she wants....you