The first one is definitely a lead hem weight, used either on curtains or to hold people's dresses down in the wind. Looks to be mid 1800s.
The second button is civilian and is probably from the mid 1800s as well but it is hard to tell with out an image of the back
Nice that there's still some gilt left on the back Mike.
Based on what I can see from your pics, I did my best to enlarge and clean them up, I think your button is relatively modern.
There's no back mark and the casting looks weak, by this I mean it looks to be crudely cast in one-piece, this indicates to me that it's likely from the mid-20thc.
I'm thinking it's European in origin, from the 1920s and probably from a suit vest or cardigan/sweater.
Hopefully someone else will chime in with their theory.
Dave