You can 'sister' the joists as long as the 22" OC is OK. If not and they need to be, say, 16" OC, then start from one end and work your way across the underside of the loft at 16" OC intervals (as is the 2x6s weren't there. Should you hit a point where a 16" mark is on a 2x6, put a 2x12 on BOTH sides of the 2x6, and continue on at the 2x6 to the next 16" mark.
I say go w/2x12 for better support. Also, I'm assuming the underside is exposed or simply drywall. If there's duct work and/or electrical and/or plumbing under or between the existing joists, you'll have more work. DON'T cut out any 2x6 joists until you have all the 2x12s installed. My best to ya and hope this helps.