Welcome to the Apple Discussions. Are you publishing to a non-Mac hosting service? If so then create a permanent folder on your hard drive and publish to it.
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Then use the free Cyberduck to upload your files to the server. It's able to determine which are the new files and upload only them.
HOWEVER, do not delete any of the files in that permanent folder after you've uploaded.
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They must remain so the next time your make edits and publish just the changes via the File->Publish Site Changes menu option only those new files will be published to that permanent folder. Then Cyberduck can do it thing again.
Another application that can upload only changed files is
Web Site Maestro. It optimizes the site files reducing the site's size by up to 48% or so making loading of the site in browsers much faster.
Happy New Year