in my experience. BB height affects stability of your ride, but mostly while standing on the pedals since you weight is then directly on the BB. but raising it 7mm may or may not make a difference in your ride. however, raising it ABOVE the axle height will make a dramatic difference in stability. BMX bikes are incredibly nimble (aka unstable) due to them having a BB higher than their axles, where as 29'ers will feel solid as a rock since they have a dropped BB height relative to their axles. it has to do with torque applied while standing. (i know wheel size also plays a factor but we're assuming spherical cow here). so considering that the DROP or RISE from the axle height affects the ride more than height, a 13in BB height on a BMX will feel much different than a 13 in BB height on a 29'er.
my track bike has a BB height equal to its axles, and its nimble and fun to ride, where as my road bike has a BB drop height relative to the axles and feels like a cruiser in comparison (both on 700c rims).
TL;DR higher BB, in relation to axle height, means a more nimble bike, lower BB is a more stable bike. especially while standing.