I haven't done sweatshirts but I have done t-shirts & if you use tearaway & a dense design, it doesn't hold up as well after many washings (6-7)but if you use cut away then it works great as it stabilizes the design & when needed I use a wss on the top of the design. Hope this helps, Hugs Loralye

The Mesh you are thinking of is a No Show Mesh or the newer product No Show Diagonal Mesh.
They both come in a Non Fusible or Fusible version

Both are Cut Away stabilizers but are light weight.
You can use 1 or 2 layers depending on the stitch count of the design you want to stitch on the item.
You can also float a piece of Medium Weight Tear Away stabilizer under the hoop in combination with the Mesh stabilizers to give better design definition and design support.

The newer No show Diagonal Mesh while hold about 12,000 stitches per layer.

Here is one link to a discusion on the subject here on the forum.
EastWitch2

Here is another link to more discussion on stabilizing T-shirts.
Check the link in this thread for the Floriani website as there is lots of information on how to stabilize knits on it.

Floriani link to information on how to stabilize knit type fabrics such as T-Shirts.
Scroll down and read and see the pictures.
Click each picture on the right side of the page for a close look of each

Here's another link to a question that may help you, asked yesterday.

i have found that i get good results if i use the mesh on the back and a layer of wss on top.