.. Why does Gregor's role in the play keep getting bigger?

Because Thanos is needed to load the stolen art into trucks, so Grigor has to fill in the gaps in the play so no one notices that Thanos isn't on stage. Also, Xenia and Thanos are starting to realize that Grigor isn't wholly committed to the heist, so they're slowly shutting him out of the process. By the end of the game, it's clear that their intention is to slip away at the end of the play and leave Grigor and Niobe to take the fall. Definitely not nice people.