The history of Abijah's reign is here related far more fully than in Kings (marginal reference), especially as regards his war with Jeroboam.

Now in the eighteenth year of king Jeroboam began Abijah to reign over (a) Judah.
(a) He means Judah and Benjamin.

Now in the eighteenth year of King Jeroboam began Abijah to reign over Judah.; see Gill on 1-Kings 15:1.

Jeroboam and his people, by apostacy and idolatry, merited the severe punishment Abijah was permitted to execute upon them. It appears from the character of Abijah, 1-Kings 15:3, that he was not himself truly religious, yet he encouraged himself from the religion of his people. It is common for those that deny the power of godliness, to boast of the form of it. Many that have little religion themselves, value it in others. But it was true that there were numbers of pious worshippers in Judah, and that theirs was the more righteous cause. In their distress, when danger was on every side, which way should they look for deliverance unless upward? It is an unspeakable comfort, that our way thither is always open. They cried unto the Lord. Earnest prayer is crying. To the cry of prayer they added the shout of faith, and became more than conquerors. Jeroboam escaped the sword of Abijah, but God struck him; there is no escaping his sword.

The commencement and duration of the reign, as in 1-Kings 15:1-2. Abijah's mother is here (2-Chronicles 13:2) called Michaiah instead of Maachah, as in 2-Chronicles 11:20 and 1-Kings 15:2, but it can hardly be a second name which Maachah had received for some unknown reason; probably מיכיהו is a mere orthographical error for מעכה. She is here called, not the daughter = granddaughter of Abishalom, but after her father, the daughter of Uriel of Gibeah; see on 2-Chronicles 11:20.
(Note: Against this Bertheau remarks, after the example of Thenius: "When we consider that the wife of Abijah and mother of Asa was also called Maachah, 1-Kings 15:13; 2-Chronicles 15:16, and that in 1-Kings 15:2 this Maachah is again called the daughter of Abishalom, and that this latter statement is not met with in the Chronicle, we are led to conjecture that Maachah, the mother of Abijah, the daughter of Abishalom, has been confounded with Maachah the mother of Asa, the daughter of Uriel of Gibeah, and that in our passage Asa's mother is erroneously named instead of the mother of Abijah." This conjecture is a strange fabric of perverted facts and inconsequential reasoning. In 1-Kings 15:2 Abijam's mother is called Maachah the daughter of Abishalom, exactly as in 2-Chronicles 11:20 and 2-Chronicles 11:21; and in 1-Kings 15:13, in perfect agreement with 2-Chronicles 15:16, it is stated that Asa removed Maachah from the dignity of Gebira because she had made herself a statute of Asherah. This Maachah, deposed by Asa, is called in 1-Kings 15:10 the daughter of Abishalom, and only this latter remark is omitted from the Chronicle. How from these statements we must conclude that the mother of Abijah, Maachah the daughter of Abishalom, has been confounded with Maachah the mother of Asa, the daughter of Uriel, we cannot see. The author of the book of Kings knows only one Maachah, the daughter of Abishalom, whom in 2-Chronicles 15:2 he calls mother, i.e., גּבירה, i.e., Sultana Walide of Abijah, and in 2-Chronicles 15:10 makes to stand in the same relationship of mother to Asa. From this, however, the only natural and logically sound conclusion which can be drawn is that Abijam's mother, Rehoboam's wife, occupied the position of queen-mother, not merely during the three years' reign of Abijam, but also during the first years of the reign of his son Asa, as his grandmother, until Asa had deprived her of this dignity because of her idolatry. It is nowhere said in Scripture that this woman was Abijam's wife, but that is a conclusion drawn by Thenius and Bertheau only from her being called אמּו, his (Asa's) mother, as if אם could denote merely the actual mother, and not the grandmother. Finally, the omission in the Chronicle of the statement in 1-Kings 15:10, "The name of his mother was Maachah, the daughter of Abishalom," does not favour in the very least the conjecture that Asa's mother has been confounded with the mother of Abijah; for it is easily explained by the fact that at the accession of Asa no change was made in reference to the dignity of queen-mother, Abijah's mother still holding that position even under Asa.)