Would you say it is hot and sunny, or shady and moist, or something in between?
As you saw from weeds, once a seed gets there, it can do surprisingly well as the roots creep down.
If hot and sunny, a creeping sedum would probably grow well along the gap.
If moist, I'm imagining little pansies/Johnny Jump Ups/ violas.
Those are just my first ideas, knowing nothing about your climate.
But you DON'T want anything with strong, woody roots that may damage the tile or grow too big. Many 'perennials' might have roots like that.
