Wrong workflow. You did not resize the shape, you scaled it and scaleis a transform property that is applied to the whole shape group. There's a difference between actualyl changing shape parameters like width and height or moving the anchor points of a freeform path vs. just selecting the group and stretching out the transform bounding box. I suggest you really take your time to understand this stuff and read the help rather than spending endless hours watching bad tutorials. With a proper understanding of how to structure and reorder your shape groups they can be a powerful tool, but pardon the directness, just mucking around will not give you the results you want in a controlled fashion.
I'm with Mulenium on this 100%. You scaled your pen tool drawn shape layer and you should have transformed the path. If you are working with rectangles you should not be using the Pen tool, you should be using the Rectangle tool and a shape layer, them modifying the properties of the rectangle. Draw one, press the U key twice to reveal the modified properties and then start duplicating and making size and position adjustments on Rectangle 1, not on the Shape Layer.
You will know what I"m talking about if you spend 10 minutes with the help files. Type Shape Layers in the Search Help field at the top right corner of AE to find the info.
I'm perfectly ok with an RTFM answer, even when that manual is long. My problem after reading several different articles on shape layers and paths as suggested (curiously not all of which appear to be from Adobe but are linked from Adobe's help files), is that I still couldn't quite put the pieces together and figure out how to apply the stroke in a way that would apply the same width to the path vs following how it had been scaled. I did learn some things about shape layers however which is of course always good.
A couple things based on my persistence and in carefully reading the above reply from Rick.
1) selecting the points on the path that I want and moving them to stretch the shape produced the desired result - the stroke stayed the same. I understand now that I was changing the scale property in my previous workflow vs what I really wanted/should have done, which was moving two points of the path to create the desired effect.
2) removing the stroke and right clicking on the layer and selecting stroke from the layer styles also produced the desired result.