Yes you can bring Tweezers in your carry on luggage on the airplane.
I have brought Tweezers with me on the airplane in my carry on luggage and it was allowed without any issues.
According to the airlines and TSA Tweezers are permitted, as well as electric razors, disposable razors, and their cartridges.
You can also bring scissors on the airplane in your carry on luggage as well.
The scissors are allowed on the plane in your carry on luggage as long as the blades of the scissors do not exceed 4 inches in length.
If the blades on the scissors are longer than 4 inches then then scissors must go in your checked baggage.
But tweezers are perfectly fine in your carry on luggage.