<< The railing moves visibly for +/- 1 inch in the middle of the span. How does
one improve the support of railing? >>
Take the whole sorry hack job down and get a competent carpenter to do it
right. It is obvious that the posts were not securely anchored to anything at
the bottom. Check sources of deck hardware, box stores, whatever, for railing
post mounting devices to learn more. Good luck.
My railing posts go into the ground. You provided no photos but
obviously a hack built it. Get some bids and do it right. Did you get a
permit, no or it would have failed.