Yes Tweezers are allowed on the airplane in your hand luggage as well as disposable razors, scissors and nail clippers.
The only thing though that isn't allowed on carry on hand luggage on an airplane is a cork screw that opens bottles of wine.
The scissors are allowed on the airplane in hand luggage as long as the scissors blades don't exceed 4 inches in length.
For the razors if it's a straight razor you may take it on the airplane but not in your carry on luggage.