Yeah. Use one or the other. Weebly looks like its doing alot of stuff in the backend so the user is as far from the code of the website as possible, so chances are they aren't going to let you use your own code, and theres likely a fair bit of php and such like in the background that will balls up if you try to shove your own code in there.
If Hype exports all the html and assets for you, then just get a basic host and ftp the files to your server. Else stick with weebly and put up with its limitations.