As Paul describes love in this verse, it is a form of devotion to one's siblings. It is essential that we love each other with brotherly affection. Secondly, Paul urges us to compete. We are instructed to show honor to one another by outdoing each other in this regard. In the body of Christ, if each of us acted on this principle, we would always feel deeply honored by others and never feel satisfied that we honor each other adequately.
This weighty epistle by Paul to his beloved brothers and sisters in Rome emphasizes the great salvation we have achieved, our position as already justified, how we are being sanctified, and our assured future as glorified and made as glorious as Christ's body one day. Paul concludes his remarkable treatise on salvation by explaining how to live the Christian life in a manner pleasing to God.
A life such as this can be found within us through the Holy Spirit and expressed through our new life in Christ, but only those who choose God-dependency over self-dependency will be able to benefit from it. Love one another with brotherly affection and strive to outdo each other in showing honor and grace to all.

Dear Heavenly Father, my sincere thanks go out to You for Your love. Let Your love stream through my heart to all of my brothers and sisters in Christ as I pray for Your godly love to fill my heart. Give me the ability to love with brotherly affection and to put others' needs ahead of my own. Let me embrace those around me with brotherly affection and strive to outperform others in honor and grace. 
In Jesus's name I pray. Amen.