Very sloppy shifting on smaller cogs (BSO)
OK Based on comments - your BSO rear derailler is not following the contour of your cassette, and is ending up a long way from the smaller cog.

It should be like this stylised image:



Doubtless you have some wear on the cassette, and the RD position is limiting the number of teeth that are actively engaged in the chain.

I bet on the big cog you've got 5/8 of the teeth meshed with the chain (~20 teeth) and on the little 14 you might have as few as 3/8 (~5 teeth)  so this accelerates wear, and fewer teeth meshed means skipping errors earlier.

You could try a new cassette and chain, if the cassette appears worn.

The other option would be check the rear derailler and see if you can make it move more diagonally

Another possibility is that your B-tension screw is too loose, or isn't even there.