Yes tweezers are allowed onto the plane in either your checked luggage or your hand carry on luggage.
I've taken tweezers on the plane in my carry on luggage without any problem.
Besides tweezers being allowed on the plane you can also take scissors, nail clippers and disposable razors and their cartridges.
Still tweezers and scissors can be dangerous and used to stab someone with but they're allowed on the plane in both your checked luggage and carry on luggage.
You should have no problem taking the tweezers through airport security.