Hard boiled eggs are generally good for up to 1 week after you hard boil them as long as you keep the hard boiled eggs refrigerated.
Eating 2 week old hard boiled eggs is not recommended as it could make you sick if it has gone bad.
Before eating the 2 week old hard boiled eggs make sure they have no bad smell to them or any mold growth and if they do have a bad smell, bad taste or mold growth throw them out.
In my opinion I would say it's not safe to eat hard boiled eggs that are 2 weeks old because there's a potential of getting sick from them.
It's best to eat the hard boiled eggs within 1 week of hard boiling them and if you have any 2 week old hard boiled eggs they really should be thrown out to avoid risking your health.