v1, is the summation, the result of the war initiated by the hubris of Abner and Joab in 2:8 through 32: There was a long war between the house of Saul (Ish-bosheth) from Israel and the house of David from Judah. Overt hostilities resolved when David became king over all Israel (5:3), but antagonism continued long after that. Much of David’s actions that follow should be seen as trying to bridge that gap. David's house became increasingly strong, but Saul's house became increasingly weak. *By “house” here, is meant the political, military allies of each respective king, as well as his kinsmen and friends.
V2-5, The key revelation of these verses is that during the seven and one-half years that David ruled Judah, he increased in political, military and regional stature, because God was graciously blessing him. (Much of 2 Samuel, beginning with this one, plus 1 Samuel 31, are restated in 1 Chronicles.)