It has been a while since college physics but you have less [angular_momentum][1].  The vector points out from the axle and magnitude is based on velocity and weight.  So if the tire is 1/2 the weight you have 1/2 the stability.  Conservation of angular momentum is what lets a top spin.

I misread.  I thought you just changed tires on the same bike.  Bike geometry will be the biggest factor.  Head tube angle is a big factor.  Tire and rim weight is also a factor. 


  [1]: https://en.wikipedia.org/wiki/Angular_momentum