Deflection check for an odd scenario. I think I am ok to tile.

[ARCH81]

How did you 900 lbs weight tested the joist?

I piled tiles, cement, paint cans, my girlfriend, etc on the far dormer wall. That is where the halfway point of the joists are and hence the potentially deepest sag.

 

[Tile Marble Granite]

Kinda figured you did that just wasn't sure. Anyways, if I were to work on a 2 x 6 joist I would try my best to reinforce those joists to the best of my ability and keep that floor as light as possible using uncoupling membrane.

 

[Ben-gee]

Just put in a few noggins here and there, amazing how much it stiffens up a floor.