WRH,
"If you have two separate paths on different layers, and you want to merge the paths into a single closed path, how can you do that while maintaining the original curvature of one of the paths?"
In order to turn them into one path, you will have to live with the fact that it ends up being on the topmost Layer.
Smart Guides being your friends (telling you when you are within snapping distance), you can:
1) Make sure the end Anchor Point of the blue path is on the green path;
2) Select the green path, then with the Scissors Tool Click on top of the end Anchor Point on the blue path (you can move the cursor along the green path Smart Guides saying path until you reach the spot where it says anchor or intersect);
2) Delete the unwanted end of the green path;
3) Click an empty spot with the Direct Selection Tool, then ClickDrag over the hopefully coinciding end Anchor Points to select them both, then use Object>Path>Average and choose Both;
4) Hold Ctrl/Cmd and press J to join the two paths, and choose Corner.
The Object>Path>Average part in 3) is to ensure that the end Anchor Points are really coinciding, to avoid two separate Anchor Points close to each other. It may be unnecessary if you have made a true hit in 2), but if you have, no harm is done.
The Corner part in 4 is to avoid the inevitable change of shape curvature if the Handles have different directions. It is unnecessary, and you can use Smooth if they have the exact same direction, but if they have, no harm is done. You can also try both ways on identical copies from 3) and see.
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