ATC Local Controller reported aircraft on departure climbing slowly and did not turn to their assigned heading resulting in the aircraft flying towards terrain.

Narrative

Aircraft X departed RWY XXL full length on with a heading of 280. The weather was VFR. These aircraft are generally unable the climb gradient of the published SID; so they request radar vectors instead. About a mile off the departure end; I noticed they had not yet started the turn to 280. I asked them to verify they were in the turn heading 280 and they claimed that they were. They continued to climb very slowly and turn very slowly; I called traffic on an unidentified vfr aircraft approximately 4nm to the southwest indicated at 064 as Aircraft X was still climbing out of 060. I didn't realize how close Aircraft X was to the limits of the MVA; and they may have been below it.I should have pulled up my MVA quick map once I realized how far south he was going. Additionally; I could have given a radar vector that was more north of the course they were on. I could have given a low altitude alert had I realized he might be too close to the higher MVA. I did not get a LA (Low Altitude) alert from STARS (Standard Terminal Automation Replacement System); which may have helped me to make a decisive action.