When I searched I had '1800' in the keywords so 18th century is all I can say for now. If you scratch or scrub a little area with brasso you will be able to tell if its brass if you wanted to. It could be iron though.
I doubt it is a grenade as I searched for a similar looking rifle grenade of springfield and enfield and they look very different compared to the shape of your object there. BUT if you are worried, get a pin or nail and slowly scrape out the little hole as far as you can, DONT DRILL IT OUT just in case. Use a drill bit and rotate it slowly by hand, letting the junk fall out. Keep a bucket of water nearby and dunk it into that as often as you can. If it is a grenade ( which I very much doubt ), getting into that hole and soaking it will ruin any gunpowder if it were in there. If it's a plumb bob, that hole probably goes all the way through.
Even if you are super paranoid, you dont have to do this by hand, you could make a jig to hold, drill and drop in water from a distance using wood and string. If you live near me, I can do this for you if you want, but chances are we are miles apart. ( Can you update your profile so we know what area you are in? )
I just noticed in the photo I posted that maybe brass was just a decoration on the bobs, and the main section ( what you have ) could be iron.