Hi CJH
In our experience there are two ways to upload an image.
First one is via the code editor into the assets... This may be something you'd do if you were using the image in a bit of custom HTML..
The second being if you had a drag and drop image placeholder on your page. and were trying to upload using the drag and drop/click to upload features.
If you're having issue with the first, and trying to replace an image that's already there, then sometimes it doesn't Appear to have uploaded the new image (Something possibly to do with the image being cached on Weebly's servers)... but it generally is, and can be seen when republishing the site (just may take a while to update in the Weebly dashboard).
If however you're using the standard Weebly drag and drop features to upload an image... Can you tell us if you're uploading over an existing image or is this a brand new image you're trying to uplaod via the drag and drop Image element.
Either way.. a few things to try are log out of Weebly. clear browser cache and reopen everything...
Also sometimes we have little issues that randomly appear to, which appear to be intermittent and browser specific so we always try switching our browser and seeing if it helps...
Hope this helps!
