Original images are never touched. You can resize during Export.
To build on what Rikk Flohr said:
Lr is non-destructive, which means the source image stays forever the same - the exported image can be anything you want (cropped, resized, etc..).
If you truly want to overwrite your original, just export n' add to catalog, then delete original. Optional, if applicable (e.g. export is same file-type as original): rename the exported file to match original. Such is NOT recommended under normal circumstances, but some people want to do it sometimes..