you need a woven stablizer (which comes in fusable or sew in) NOT DOUBLE SIDED FUSABLE WEBBING LIKE HEAT & BOND!
the stablizer has fusable on one side (the side fused to the back of the t-shirts - is a lightweight (fabric) which will keep the knits from stretching out of shape.
paper backed fusables are used for appliques---and can be quite stiff- are not the product you are seeking.
Pellon makes a number of stablizers- as does sulky- i'm sure there are others. they would be in a sewing department---used in garment construction- available in different weights- stay soft (they are fabric)