Edit jpg in photoshop creates a huge file

I'm a bit puzzled about what you describe here. 'Edit a Copy with Lightroom Adjustments' is a dialog that you will only get if you edit an RGB file (jpeg, tiff, psd), not if you edit a raw file. But when you do that with Photoshop as primary editor, then you will not get another dialog where you can specify file format, color space, bit depth and resolution. This is the dialog for 'Edit in Photoshop':

The copy that opens in Photoshop will not be a jpeg, but a tiff or psd. That, including the color space and the bit depth, is specified in 'Preferences > External Editors' and jpg is not an option, only tiff or psd are. So even if your original file is a jpg, the copy could be a 16 bits TIFF, which explains the huge size. Don't be fooled by the file name that Photoshop shows, ending with .jpg. That's because the Photoshop file has not been saved yet, so you'll see the original file name, even if the image in Photoshop is 16 bits (which is not supported by jpg).

It's possible to add Photoshop as secondary editor as well. If you open an image in a secondary editor of in a plugin, then you do get a dialog with the options you mentioned. Here's how that looks for a plugin:

So did you add Photoshop as secondary editor and are you using that? If so, are you sure this link is still pointing at the most recent version of Photoshop?