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I have a .blend file. When I delete objects and save or save a copy, the file size continues to grow not shrink.
For example, I have a file that is 228 MB. I need to be under 200 MB to import to Sketchfab. So I delete a few objects but the file size never changes. In fact, I can delete all objects and that has no effect on the saved file size.
What is the proper way to purge objects from a model?
The outliner should tell what's in your file. And it has different Display Modes that can tell you different things.
One I would be curious to look in your file is the Orphan Data:
On a new scene, you should see only the default Brushes and the Viewer Node's Image:
These are technically "unused" but are marked with a fake user so that Blender doesn't get rid of them when reloading the file.
Maybe some of your meshes or other data that you don't need are still there. In which case, you can uncheck the Shield icon, then hit the Purge button (which does the same thing as the menu File > Clean Up > Unused Data-Blocks) to remove every unprotected orphan, and save again.
When you purge, some data blocks might become orphans because of the purge (for example, image textures in a material). Hence, you might see new orphans after a purge. In that case, you can either keep spamming the Purge button, or use this menu instead:
Another interesting Display Mode is the Blender File.
Here you could see most of the data blocks you can ever need (unless you're programming something, then it's probably the Data API Display Mode that interests you).
If for example you have linked or imported some data, it will be displayed there. You can select things and 
RMB > Delete.
I would check the orphans data after cleaning there, just in case.
If you have used scenes, view layers and whatnot, some objects might have been hidden from you on the default outliner's display mode or viewport, but this will show you everything regardless.
This could also be an occasion to look for duplicates, both in objects and data, to see if the duplicated objects could have shared the same data instead of each having a duplicate of the same thing, or other oddities that could be optimized.
Also as a side note:
Since your goal is to lighten your file for uploading on sketchfab, then you could in theory delete some of the stuff sketchfab doesn't need either. Like brushes, screens and workspaces. It will not make a huge difference, but it could.
Since your file gets bigger when adding and deleting objects, maybe you have this option turned on under the menu File?
Maybe try turning it off and see if that occurs again.
Then finally, the ultimate way to reduce the file size is to compress it using File > Save As > enable compress in the explorer's sidebar:
If you don't see that sidebar, click the little < arrow on the right border or press N.
