Depends what you mean by "the more you save them" and "more compressed".
Each time you open and resave a file, there is a loss of quality.
That loss of quality includes detail loss, and less details means that the file is easier to compress (i.e. smaller).
If you save multiple times a file without closing it, it is like if only last save counts.
That's why the JPEG conversion should only be done at the end, after resize/cut operations.