John Gill Commentary 2 Samuel 19:33

"And the king said unto Barzillai, Come thou over with me, and I will sustain thee with me in Jerusalem." — 2 Samuel 19:33 (ASV)

And the king said to Barzillai, come you over with me
Over Jordan; Barzillai came with an intent to accompany the king over Jordan; but the king meant not only to go over Jordan, but when over to go further with him, even to Jerusalem:

and I will feed you with me in Jerusalem ;
meaning, that he should dwell with him in his palace, and eat at his table, in return for feeding him at Mahanaim.