Albert Barnes Commentary 1 Kings 12:16

"And when all Israel saw that the king hearkened not unto them, the people answered the king, saying, What portion have we in David? neither have we inheritance in the son of Jesse: to your tents, O Israel: now see to thine own house, David. So Israel departed unto their tents." — 1 Kings 12:16 (ASV)

See the marginal reference. The words unmistakably breathe the spirit of tribal jealousy and dislike (1 Kings 11:40 note).

Now see to your own house, David — that is, “Henceforth, house of David, look after your own tribe, Judah, only.” It is not a threat of war, but a warning against interference.