Are there any dangers to sistering a joist with oversize lumber?
The reason that joists are sistered using the same height of wood is simply space; generally there's no extra room. If you've got nothing below and there's space then there's no reason you can't use a taller piece of wood. Things to keep in mind:


Spanning as much distance as you can so you transfer the load as evenly across the original joist. If it's too short it's going to still bow, just in a different spot, and you'll add additional stress on the existing joist. 
Don't weaken the original joist by drilling holes or cutting
You'll need to raise the joist into the correct position before you glue and nail, otherwise you'll just solidify it in a sagged position! 
Prepare the surface of the old joist properly for gluing if you want it to take