I agree with the replacement suggestion, because it isn't only the balance, and the repair being right due to inexperience or the unknown metal, but why it originally failed, and by welding it you most likely decreased it's strength (which apparently wasn't good enough to start with).
Another thought... If the chuck originally failed with a 5 pound part in it spinning at 300 rpms, and you put a 10 pound part in it some years later after it has been repaired and spin it at 250 or even more, isn't it going to want to fail again?
I think that this is how people get hurt...
You go ahead and repair it, and only use it for a welding positioner although it still fits your lathe. After your death, your heirs sell the lathe and all of the attachments at your auction. The guy sorting the stuff for auction puts the repaired head in the lathe pile, not the welding pile. A novice buys it, and because he doesn't like the looks of your weld on "his new machine" fills and paints the weld so it looks good, and then he passes away. Your Son or Son in law buys it back because "it was yours". He spins the lathe chuck too fast, it comes apart and kills him. You get blamed for the death because somebody remembered that you repaired it.
Write this scenario any way you want to but none of it will be pretty.
David from jax