A friend loveth at all times, and a brother is born for adversity. The two halves define each other. Anyone can love at some times — when it is enjoyable, when it is reciprocated, when the friendship costs nothing. The proverb is interested in the other times.
Born for adversity is a strong phrase. It suggests a relationship that comes into its own precisely when things go wrong, the way a tool that has sat in a drawer turns out to be exactly what the job needs. Some people are only fully themselves in a crisis, and Proverbs counts that as a high compliment.
The verse a few lines earlier is worth reading with it: He that covereth a transgression seeketh love; but he that repeateth a matter separateth very friends. Repeating a matter — bringing it up again, telling someone else about it — is named as the specific thing that ends friendships. Not the original offense. The retelling.
Most of us have more acquaintances than we can count and fewer friends of this kind than we would like to admit. It is worth asking which we are being. Loving at all times is unglamorous work: turning up when it is inconvenient, staying past the point where the conversation is comfortable, and declining to repeat what you know.