The service ceiling of the SR-71 is still well beneath the altitude of a modern balloon. The speed isn't necessary, and it's altitude record has been beaten by other modern jets.
If we're spitballing solutions, balloons are slow, fragile and move in relatively predictable paths. An F-15 could reach the same altitude, and launch it's own balloon with a small solid-fuel booster that also corrects the trajectory. If the interceptor balloon could get within 1-2km of the target balloon, then a cheap kinetic weapon firing HEI projectiles might be enough to destroy it.
If we're spitballing solutions, balloons are slow, fragile and move in relatively predictable paths. An F-15 could reach the same altitude, and launch it's own balloon with a small solid-fuel booster that also corrects the trajectory. If the interceptor balloon could get within 1-2km of the target balloon, then a cheap kinetic weapon firing HEI projectiles might be enough to destroy it.