The thought just occurred to me, love covers a multitude of sins (1 Ptr 4:8) because love forges through the great chasm sin creates in a given relationship.
Whatever else sin does, it severs a relationship. If I were to sin against you by, say, lying to you, I would have provided a legitimate reason for you to forsake our relationship and kick me to the curb. You would be completely justified in doing so.
But if you were to respond with love, you would push past the gulf between us and resurrect the relationship despite the offense. The result is that the sin itself is covered – canceled out, in effect. In love, the relationship is the thing worth protecting at all costs, not the rules.