William Burkitt on Romans 13:8

Our apostle having finished his exhortation to duty towards our superiors, comes now to enforce the duties which we owe unto our neighbours; the first of which is, to render and pay to every one what is due unto him. Moral duties are mutual debts which we owe one to another; one of which namely, that of love, we can never fully discharge, but must be ever paying, yet always owing: Owe nothing to any man but love, implying that must be always owing.

The truth is, this debt of love is so far from a possibility of being paid on earth, that it is due in heaven to God, angels, and saints; There abideth charity, 1Cor 13:13. All other debts may be paid whilst we live; but this of love cannot be satisfied while we live.

Observe next, The argument, reason, or motive, to excite unto this duty, and that is drawn from the excellency of this grace of love: He that loveth, hath fulfilled the law; that is, he that loveth his neighbour as he should and ought to do, in deed and in truth, out of a pure heart fervently, he hath fulfilled the law, that is, the law relating to his neighbour, the duties of the second table are fulfilled by him.