Piper J3 Cub pilot reported a loss of directional control after landing and struck a taxiway sign and light before coming to a stop. Pilot reported observed wind direction differed from METAR at times.

Narrative

A short time after landing; the airplane started a slight right turn. Before I could get the plane turned back down the runway; I was off the right side of the runway; in the grass. I hit the taxi way identification sign; and a taxi way light. Both lights broke of their supports.There was damage to the airplane landing gear and a tear in the underside of the right wing about 2 inches past where the strut connects to the wing. Once the airplane came to a stop on the taxiway; I was able to control the airplane normally and taxied to the using normal taxi procedures. I spoke to 2 A&P's and after some small repairs; was satisfied that the airplane was still flyable and flew the aircraft to the next stop in this flight. I had no issues flying or landing the aircraft to its final destination.The METAR at ZZZ indicated calm winds. The calm wind runway is Runway XX. There was an aircraft that took-off about 5 minutes prior to my arrival. They took off on Runway XX. As I approach the runway; I noticed that the windsock on the left was facing the opposite direction; but the sock was not indicating no wind. It was flat.After taxiing to the ramp; I eventually noticed a wind; of a less than 5 kts; coming from approximately 120 to 130 degrees. The wind continued to build to about 8 to 10 kts. Then died down later.