I flew with a duffel bag full of tools. I had to fly to Carolina to help fix my mothers roof. I took a sawzall, skill saw carpenter tools, including drywall keyhole saw & razor blade knife. As long as your bag is under 50 lbs you should be fine. Actually, my buddy came & brought some tools too. We had to make some adjustments because one of the bags were overweight , the other was under so we took some tools out of one bag & put 'em in the other. We had no problems at all.
Side note- My friend fly's to New York to go hunting & checks in his guns. After checking in the guns, he gets to skip the security area & gets escorted straight to the gate.