There are a number of issues with a stock Ninjette that could affect how stable it feels. I'd put tire width at the end of that list.
- The springrates are mismatched. (Front, Rear)
- There's a good chance neither springrate matches your weight.
- Stock tires are bias-ply.
- Stock tires are known more for longevity than performance.
- Stock 2012 tires are nearing the end of their useful life now, regardless of their mileage.
- Little Ninjas are known for weak, flexing frames.
I have a 150/60 on my wider aftermarket wheel. I switched from a durable bias-ply tire to a performance radial, so it definitely feels different, but I'm pretty sure the extra 20mm has minimal to no effect.
Here's what going from a 130/70 to a 150/60 looks like.
Keep in mind that going to a wider tire on a wheel that's too narrow will actually pinch it in, causing the profile to be altered, which can lead to less tire in contact with the ground. The 300 uses a 140 rather than a 130, but it also has a wider wheel.
A 150/60 is also getting close to fitment limits. People have had trouble with certain tire models in that size just due to spacing issues from using a different sprocket size.
In my opinion, springing the bike to match your weight and getting modern radial tires like the
Pilot Street will do a lot more for you than getting an extra pencil-width of tire.