Attic Floor Joist - Structurally Secure
Yes, you can sister 2x6 joists, but you have a few problems:

1) Code requires 40 lbs. per square foot live load plus dead load. 2x6 joists at 16” will span 12’ and support a floor live load of 40 lbs. per square foot plus a dead load of 10 lbs. per square foot. However, they need to be “Select Structural “ grade or better. 

2) The existing plaster ceiling will crack with very little deflection from the weight of the floor. So, I’d isolate the floor load from the joists that support the ceiling plaster. In order to do that, the new joists need to be about 1/2” above the plaster, not attached to the existing joists and the top of the new joists needs to be 1/2” above the top of the old joists so when the new joist deflect the floor sheathing won’t touch the top of the old joists. (New 2x6 joists are going to be about 1/8” smaller so make sure you account for their size...)

Btw, the minimum ceiling height in a room is 7’, unless you have a sloping ceiling. Then a portion of the room can be under the 7’. 

I’d add a couple of extra joists under the tub/shower too. 

Btw, no waterbeds.