Gemini do you actually mean the width or the tyre profile as I can't see why the width would make much diff?
Correct rim width ensures flex at the designed flex point in a tire sidewall for optimum tire performance.
If the rim is too narrow, the flex point moves toward the shoulder area, creating heat buildup in the shoulder.
If the rim is too wide, the flex point moves towards the rim area, causing heat buildup in the lower sidewall.
Wider rims may offer some performance advantages over narrow rims. A wider rim increases the distance between the beads, which results in a straighter sidewall, which stiffens it. This results in quicker steering response and higher cornering forces.
Negatively, the straightened sidewall transmits more road shock to the wheel and suspension, placing greater stress on chassis and suspension parts and delivering a harsher ride. The straighter sidewall exposes the rim, making the wheel more susceptible to damage.
A narrower rim pulls the beads closer together, curving the sidewalls. This increased curvature allows the sidewall to flex more readily over bumps and absorb more road shock during driving. This offers a softer ride.
Hope this explanation helps.