How do I tighten this adapter so it stops leaking?
Under that brass nut is a copper or plastic ferrule (sometimes called an olive) if the inside of it is scratched it will not seal.They are cheap so replace it.
Make sure the end of the pipe is smooth and has no spurs that could scratch the new ferrule. If the pipe has shrunk from the pressure of the old ferrule cut that part of pipe off clean up the cut edge and fit a new ferrule.

Plan B: Is if that upper hose is long enough replace the short copper pipe with a connector, seal the connector to the valve and the hose with thread tape.