Pilot flying DA 40 aircraft reported engine malfunction after takeoff. Returned to departure airport.

Narrative

On DATE while taking off from ZZZ; I experienced engine trouble on the climb out from ZZZ. I noticed when I was accelerating down the Runway and obtaining airspeed the engine seemed to be a little labored. I was able to rotate and get off of the ground but when I started to climb I could not build airspeed and proper climb rate. The stall horn was constant and I had to level the plane to keep from going into a stall. I was able to add very little pitch and make a right turn to head back towards the Runway. As I was making this slow turn; I had transferred over to ATC Departure and advised the Controller that I was requesting priority handling due to an engine malfunction and needed to land immediately. The Controller advised he was contacting ZZZ Tower and to switch back to that frequency. I switched back to Tower and the Controller was able to clear the airspace so I could land back at the airport. While making these transmissions; I was only able to obtain and additional 200 ft. above AGL. The engine was still laboring and my airspeed would not increase. I went through the checklist and the systems of the aircraft. The Flaps were at the proper setting for takeoff; the trim was set for takeoff; I had full rpm and manifold pressure. There was no ice or debris on the wings. The preflight procedures had no issues with runup or engine malfunctions.