He runs into Harry as they are clocking out for the day and he is hit by a crackling tension in him, an ache, raw and dismal, that may have been mounting when Kim wasn't looking or may have crashed at once, as realization are wont to do: now that they are back into the fray, away from their little bubble of an investigation at the end of the world when it was just them making their own rules, the detective is stretched thin by a job that sees a dead man in his eyes and expects him to bend and twist and fit a strange mold that's all edges.
Something in there is about to break along old frayed lines, a cyclical tragedy long in the making, and Kim makes a guarded offer to go grab a bite together, knowing full well that his own cautiousness is a ruse, that he won't let Harry risk a relapse in the solitude of his apartment.
So if that means staying the night, so be it, if it can give Harry some space to be vulnerable and unwound and safe, so be it, and if someone has to struggle against the temptation of doing something really, really stupid tonight, let it be Kim, and he'll see this through.