I've been thinking about this, and the problems we encountered trying to deal with a similar problem (saggy ceiling in kitchen). One big issue is getting the new boards in place. With 16" on center, the longest measure you get is the diagonal between them. You will find that you can't cut the board very long or you simply will not get it up there. I'm not sure about the logic of weight on the middle not transferring to, and putting stress on the ends of the board. I would expect without additional support, eventually the 2x10's will develop cracks. May not be in the time you own the house though. Someone had used 2x6's for the roof on our den, and cut the bird mouth wrong - actually it's more likely they needed boards 14'5" and didn't want to spend the money on longer ones. Boards would have been fine except for the notch that effectively changed them to 2x2's. The ones on the ends of the roof were fine, all those in the middle had serious cracks. Roof had a nice bounce in the middle. It probably had been that way for years and years, and probably would have not been a problem for years and years to come. But we are fixing potential problems as we find them. At least the roof does not flex when you walk on it anymore. If it were my place, I would consider finding joist hangers (or modifying some) that could be used to lap over the sill plate, and support the bottom of the 2x10. I'd also put them in the middle between the 2x6's. A palm pounder is a great tool for nailing joists supports in place. You may also find the there is a bow in the floor/ceiling already, and you may have to jack up the middle to get the other boards in place. If you have a straight 2x10 and a bowed floor, you will have a heck of a time trying to get it in place. We have two support poles with adjustable ends (use a big wrench) and we've used them a few times to get roof lines back in place. We are rehabbing the entire house, and have run into a lot of "interesting" situations to deal with. Another option might be engineered lumber. I know it can be a lot stronger for the width than regular boards. Don't know what is available, just a thought. Cathy Here is a link that might be useful:

Thank you sweet11395 for clarifications. Yes, your understanding is 100% correct!!! I was referring to the rim/band joist of the house (sorry, I am still learning the decking vocabulary). I have a 2x12 under the threshold door. I am in the "design" phase. I plan to use a 2x10 for the ledger (the deck will be 21'x14'). The problem is that my wife wants the decking to be about 4" below the door threshold. If I add 1.5" for the decking and 9.5" for the ledger, I end up with 1/3 of the ledger over the foundation. I was wondering if anyone has seen a ledger bolted to the band joist and foundation. Any ideas/suggestions? I want to thank you all for your help!! I really appreciate it.

Alert, Long Post: Thanks Renovator, Worthy, Sombreuil_mongrel, Brickeyee, Weedyacres, Sierraeast, and last but not least, Pam. Ok, the big picture. I have a plan to use slate tile in a Versailles pattern ranging in size form around 6x6" or so, up to maybe 12x16. This is an estimate. This is called the "Small Versailles". The stone varies a bit in thickness and is hefty. It is slate stone from "The Tile Shop". We have a store in the metro area of Des Moines, Iowa. I will be installing this myself. My goal is for the floor to tolerate: 1) the weight and stiffness of this tile & it's underlying compound 2) fair amount of foot traffic 3) 5.5' cast iron tub 4) water for tub 5) vanity with large cast iron sink 6) toilet. 7) I might put tile on the wall and don't know if that extra weight matters. Floor as is: 1) Floor dimensions in finished bathroom is 6.5' x 9.5'. 1) 2x8 joist at 21"OC, about 10' or 11' in length, and about 9.5 free span. See picture above. 2) 3/4 (or 1") x8" subfloor. And I correct my earlier mistake, it is NOT T&G. 3) 3/4" fir T&G flooring but is covered with a layer of linoleum. When I am ready to remodel the room I will remove the linoleum. I had planned to lay 3/8" exterior grade plywood as an underlayment down on top of the 3/4" fir flooring, leaving all of my flooring intact. I will keep the bath where it is at the far end of the room (you can see the green pipe at the top of the pic). The size, either 5' or 5.5' depends on how the joist position turns out. I will move the sink to the Rt side, where the heating duct comes in. I will shorten that duct span to bring the vent closer to the front of the room (even closer to the top Rt hand corner of the pic). I will move the toilet a few feet towards the far end, about where you can now see the exiting sink plumbing on the left of the picture. I had plans to use self leveling compound and maybe imbed an electric floor/tile heating system ontop of the underlayment. This heating system is only for the tiles not to provide primary heat to the room. The room is ducted for forced air heat. Next, over the underlayment with self leveling compound (and possible heating system), lay Ditra. Then, as I understand it, I am ready to tile as per usual. As stated above I will be using 6x6 up to approx 12"x16" tiles randomly placed in the design. Bottom line is that I want a floor that will support my tile and fixtures in the BR. With all of the posts above it sounds like I need to do something, or nothing, to the floor joist system (except to get those hangers in there). I am leaning towards adding joist inbetween the existing one in the middle. The spaces between the exterior joists, sitting on the sills, and the 1st free spanned joists on either side, might be a problem because of the plumbing, especially on the left where the toilet is (out of sight in this pic). So I might have to leave that area without extra support. Or maybe I could brace around the toilet to stiffen up that area. While the Rt side might be tight, I still might be able to get a joist in there. Anyway, that is my current rendition, taking all of the above discussions into consideration. Any feedback on this plan? ps, this took me FOREVER to write up!

I think removing the current deck and rebuild is the best course. My question now is if the joists are cut flush to the outside brick then can a ledger be safely added since there is just blocking between the joists and not a continuous rim joist behind the brick. Any suggestions.