Getting them to line up is easy enough since one stroke is exactly half the width of the other.
Make sure Smart Guides are switched on
Open the a Transform dialog and set the options as shown below
Select the rectangle, and in the Stroke panel set “align stroke to outside”
- Click and drag the corner until the Smart Guide shows them aligned, and do the same for the other side of the rectangle
- To join both objects as one, you can expand the strokes and join both with the pathfinder to get one object. However the strokes will no longer be editable as strokes – they will become a filled shape instead.