How are they smaller? megabytes or pixel dimensions?
Exporting to JPG files will ALWAYS compress file size in MEGABYTES. (eg a raw might be 12mB, as a JPG maybe 3mB)
A JPG file size will also vary with image detail content and the quality setting for compression.
Cropping an image will reduce PIXEL size.
How can I keep it at it's original size
Do not check or tick the RESIZE box in the Export dialog.!
Have a look here-
Check out the sky banding (stepping) jpg artifacts in the first image at Quality 0-7.!
Why does keeping the original size matter to you?
Jpeg exports will always be small than the Raw files they're generated from; but 16 bit tiffs will be condierably larger - but in itself this fact is meaningless.