I'm NOT suggesting that you read through all of this article!
http://bjo.bmj.com/content/81/10/824
However it's clearly from an authoritative source and the last sentence of the first paragraph makes it clear that ageing definitely has an effect on tear production.
This NHS link (which is a lot easier to read!) says that the problem of watering eyes "can affect anyone, but it's most common in young babies and people over 60". So, again, there's a connection to ageing.
If it becomes a serious issue for you, the treatment options are here:
https://www.nhs.uk/conditions/watering-eyes/treatment/
However it's nothing more than 'mildly irritating' you'll either have to learn to live with it or possibly take to wearing ski goggles when you're out walking.