The automatic use of a pronoun in the objective case in constructions such as 'of you sponsoring...' and 'of me wanting...' is common. Whether the objective case, or possessive case, depends on the intended meaning of the sentence:
Is it :"How about you..."? or "How about sponsoring..."?
Hey thank you for your reply.. See suppose my friend is asking me "How about a singaopre trip this weekend" Can i reply like :"How about you sponsoring it" in a casual way
He is saying 'how about you and me taking a trip to...' You, in a casual, humorous retort: "And how about you paying for it?" This parallels the 'how about you and me...' and use of the objective case 'you' places more of the emphasis on the 'you' than 'paying'.