And illustrator calls it offset path. Just be aware that when you offset it, it creates a duplicate that is either bigger or smaller over the original artwork. If it’s bigger, I generally just select all of it and use the Pathfinder tool to merge the parts. GF doesn’t like when two paths overlap, so it’s important to remember this. Also, it only works when your image is a vector, which will give you the best results, anyway.
Ideally, after making it a vector, shrinking it to the desired size, and running a test to see what needs to be increased, if the thick parts are where you’d like them to be already, you can use the direct selection tool to individually (or using Shift to grab multiple) anchor points and dragging them out to thicken parts manually.