I'm very new to AI and am still learning about curves. I would like to know if it is possible to apply transforms to the curve between two anchor points. Specifically, I would like to increase the stroke size between two anchor points but would also like to know if other operations are possible also. When I scale currently it only increases the handle size.
You can alter stroke widths in sections of paths via the Width Tool. In some cases it may not be as precise as you'd like. For example, it smooths the stroke variations between one another.
If you are looking for one section of a path that is thicker, with square, abrupt edges - you are better off duplicating that sections, pasting it on top of the original and then altering the weight of its stroke.