Why are they sagging? is the plywood or the joists rotten?

The plywood on that side appeared to never have been properly supported. It was originally a back porch.

The whole addition needs to be removed and then built properly. It needs a shed roof, joined higher up on the main house to increase the pitch. Plus, the rest of it is probably as poor quality of construction as the roof.

Yeah, agreed; but not possible.

Rebuilding so that you have a roof that won't leak and damage your home, as well as so you can use low cost roofing materials instead of expensive epdm will actually save you money in the long term. There's a difference between cost and expense.

If you could open up one end and slide in a mid-span beam that had been specified for the load, plus the extra weight of jacking into place, you'd stand a chance of salvaging what you have if you could get the point loads to ground adequately. If you did it yourself (excepting the engineering part) it would be less painful that the tear-off.
You're between a rock and a hard place on this one.
Casey

The joists may be adequate, I can't see them well enough to say, but the rafters appear to be made with undersized scrap-grade pieces as a temporary roof until a proper one could be built but was never done I don't think any mid-span supports can do the job.

JM$.02W

Thanks Casey/Randy, A friend suggested using a couple 2x6 boards, elbowing them together longways and nailing the long reinforced 2x6 to the joists, and creating supports for the rafters off of that.

Sophie is correct. It needs to be rebuilt properly. We can see the slope isn't enough to support a shingled roof and isn't stiff enough to support a flat roof. You're out of options. Its time to rebuild.

This is a house in my area with a tighter pitch than mine, they used metal roofing. I had actually thought about this.

This was during construction:

What a horrible example of roofing that is. Not to mention the building "design" and construction as well. It's gonna leak. Count on it. Both roofs shown need to be rebuilt.

I live in MS and thought I had seen plenty of kludged together country hilbillyisms, but sheesh. OMG

2x4s as roof rafters and on the flat to boot. Whew.

Depending on the span, I'm with Casey. A do-over may be more cost effective.

Those are 2x6 rafters. I sure appreciate all the great advise from everyone!

"Those are 2x6 rafters." That's what I get for trying to diagnose through pictures. :)

Honestly, it wasn't the greatest photo!

This is roughly what I am doing MongoCT Very clear, I appreciate it. It's heart pine underneath, so not as noticeable.

hey now my rafters are 2x4's! seriously full 2x4's
not any of those new 1.5x3.5's! LOL!

no comment on the roof repair (replacement)
but man...you need some insulation in the attic
when you are done.

best of luck.