I am currently working on a project that uses back loop only single crochets and my yarn is 100% acrylic. The project is super stretchy and I am wondering if it is the stitch or the yarn or both that causes it to be so stretchy?
It's a mix of several different aspects.
The yarn can stretch a tiny amount, but that tiny amount can accumulate in a crocheted or knitted work. Acrylic and wool yarn are the most stretchy ones, while cotton doesn't stretch much at all.
The technique drastically influences how the fabric stretches. Plain weave fabric doesn't stretch at all along the grain line, but plain knit fabric (like jersey) does. Single crochets are usually very tight and not stretchy, but double and triple crochets get more and more stretchy. There is no general rule that defines stretchiness. Many patterns with holes (like ajour or knitted lace) tend to stretch more than plain patterns, but then there's patent knitting which looks very plain but is the most stretchy knit I have ever seen.
The tool size (hook or needle) in comparison to the yarn size and how tightly you work influence how tight the resulting fabric is crocheted or knit. A loosely worked fabric can stretch more, simply because there is more yarn in each stitch that can be pulled around. If you want very tight fabric, use a 1 - 2 size(s) smaller hook and keep the working thread under more tension while you crochet.