TRACON Controller reported an aircraft made a wrong turn resulted in entering a higher MVA. The controller issued a climb to the aircraft.

Narrative

Working ZZZ arrivals. Gusting winds and wet conditions causing confusion and distractions. Advertised runway is not acceptable to certain aircraft due to aircraft performance. Outside of ZZZZZ on the arrival about 20 miles from the airport Aircraft X speaks up and says they are too heavy for any runway!!?? I asked the pilot intentions since other aircraft on frequency were asking for Runway XXC. He asked to be broke out and crunch some numbers. I broke the pilot out; a left turn 180 and maintain 3000. The instruction was well before the ZZZZZ1 Tower MVA of 3300 ft. I went to work other traffic. Aircraft X makes a call at ZZZZZ2 asking if it was a right or left turn. I restated it was a left turn. Aircraft X was already in a right turn; then says he'll correct to the left making an even wider turn into the MVA. I issued a climb to 3300 ft.Company A flies a plane than cant land at ZZZ [which is] unacceptable to have an aircraft unable a Runway XXL with winds 220 @ 9 with gusts. The rate should be significantly reduced if the primary user of the airport can't land the primary runway.