I have created a shape using the pen tool and I all looking to have each line segment (from one point to the next) be a different weight. Is there a way to do this? I tried the direct select but it is selecting the entire object. Thanks!
The Scissor tool is great for this. The default hotkey is "C".
You can click anywhere on a path (in your case, on each anchor point) to effectively cut the path in that location, resulting in two paths. After that, you can simply direct select (hotkey "A") each path segment and adjust the stroke accordingly.
If I'm not mistaken, are you asking about changing the width between different anchor points in the shape? Something like the image below? One way to change the width of the stroke between anchor points is by using the width tool You can make it wider or thinner by going to a point where you want the change to start and hold-click, then moving up or down for changes