A constant windA constant wind must cause a constant accelerating force, it's the law, that's what 'wind' is- changes in pressure in the surrounding, supporting fluid which exert forces on objects which have aerofoils canted at the right angle
The balloon/object has inertia and tends to maintain the same airspeed after the last push, when in the next moment it receives another push from the constant force. Balance or imbalance between: the object's inertia keeping the object moving without any forces acting- and the slowing down due to friction (drag)
Only friction stops any balloon achieving Mach 2. Or thereabouts

Only in a vacuum would a crosswind have no effect on a supported object, that's why aerofoils. If you could support the object in a vacuum that is, but this is a thought experiment so that's not going to work

Ming