What I love about using the fleece backings, and I've made over 100 with them, is that you only have to quilt to stabilize the top and backing together. No worries about a middle layer that might shift or ball up. You can quilt as little or as much as you wish, even going so far as to outline a 12" square with no other stitching within it.
I agree about the thin fleece being harder to work with, but generally you won't find that for sale in a fabric section. You will find it in thrift stores, hemmed with a logo of some sort on it. Just be cautious when shopping there to check the fleece for density and stretch.

When selecting fleece look closely at it, if you can clearly see the base fabric knit threads, it is not a good choice.

I've done about 30 -40 quilts with fleece from JA's. Never had a problem, not stretching. BUT...I hand quilted them, so maybe that made th difference. goodluck

I used fleece and no batting. Flannel and fleece should make a nice warm quilt. Like others before me have said spray or glue basting will help with the stretching. Using your walking foot and a longer stitch length is also what I did. But I must say I like the idea of tying it. Another suggestion would be primitive hand sewing it with embroidery thread. A nice running stitch. You'll be surprised at how fast that goes. Also I know I'm cheap but I bought my fleece from the dollar store. It worked! Wish I had a picture but to many times I pass my quilts on without a photograph

I have used fleece. I like the anti-pill fleece. I like to buy something with a design of some sort on it. I found that on the plain fleece or plain fabric for that matter my mistakes in FMQ show up more.

I have backed several quilts with fleece blankets from Walmart and Target. I stock up on the blankets when they go on sale ( last year purchased top of the line King-sized blankets for $15 which I cut down to size as needed: throw, baby, or pieced for larger! I have also purchased fleece from the roll at Hancock's and JAF... just be careful because not all fleece is the same quality! My son's favorite quilt is made from pieced denim on the front with fire-engine red fleece for the back... he loves the weight!