I don't envy you.
There are several ways to remedy the situation and the chosen method IMO is unque to the actual situation which may be different depending upon how the arbor is held in place in the frame and upon how loose the arbor is.
You will likely get several responses from people who have been successful at tightening up the arbor. Silver solder, Drill the frame and tap the hole for a set screw. I personally had success in just taking a center punch and tapping the little pin which (on my problem child) held the arbor in place.
You might be well advised to carefully consider each of the methods that folks decscribe to you. Then decide on the best option considering a) the actual situation in your revolver, b) your level of skill, c) the tools and materials available to you, d) whether there is enough money in your account to pay a gunsmith. (If you take it to a gunsmith, I would be very careful to tell him that you want the finished revolver to be as strong or stronger than it was when it was new. If he won't commit to that requirement you may be wasting your money and time.)
My recommendation is that at least on that revolver, stop loading with the onboard loading lever and start using a press. (Forgive my presumptuousness if you are already doing that.) This IMO reduces significantly the stress you will put on the arbor.
My reading of history convinces me that most bad government results from too much government. Thomas Jefferson