If we can cure aging, then overpopulation will become an even larger problem than it already is. I would propose to only make anti-aging treatments available to people who haven't procreated yet and on condition they get sterilised at the same time.
On the other hand, the promise of remaining able bodied until you die from an accident might reduce the number of children because you don't have to have children that take care of you when you're too old to take care of yourself.
A lot of the world can barely afford dirt cheap medicine from decades ago. They aren't going to be able to afford state-of-the-art anti-aging treatments for a long time.
Exactly, so if we don't sterilise people who get anti-aging treatments, what's to stop them from having a litter of children every century or so ?
So prepare for some very old rich people ruling the planet who will live much longer than the serfs.
But imagine a world where we have, for example, 100-120 year old rulers while the average people live 70-80 years.
That's an extreme example, and the figures have moved since that article was published, but currently a wealthy citizen of Scotland can expect an extra 25% life expectancy compared to a citizen raised in relative poverty.