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His heart was not perfect - He was an idolater, or did not support the worship of the true God. This appears to be the general meaning of the heart not being perfect with God.

He walked in all the sins of his father - Yet Abijam prepared precious offerings for the temple service 1 Kings 15:15, probably to replace vessels which Shishak had carried off, and in his war with Jeroboam professed himself a faithful servant of Yahweh 2 Chronicles 13:10-12.

Abijam's heart was not perfect with the Lord his God; he wanted sincerity; he began well, but he fell off, and walked in all the sins of his father, following his bad example, though he had seen the bad consequences of it. David's family was continued as a lamp in Jerusalem, to maintain the true worship of God there, when the light of Divine truth was extinguished in all other places. The Lord has still taken care of his cause, while those who ought to have been serviceable thereto have lived and perished in their sins. The Son of David will still continue a light to his church, to establish it in truth and righteousness to the end of time. There are two kinds of fulfilling the law, one legal, the other by the gospel. Legal is, when men do all things required in the law, and that by themselves. None ever thus fulfilled the law but Christ, and Adam before his fall. The gospel manner of fulfilling the law is, to believe in Christ who fulfilled the law for us, and to endeavour in the whole man to obey God in all his precepts. And this is accepted of God, as to all those that are in Christ. Thus David and others are said to fulfil the law.