yeah I understand the higher the wind is, the smaller it's influence is as well
do you mean the higher wind speed? or that the parachute is higher? if you mean a higher wind speed, then you have it backwards. give it a thought. if higher (stronger wind) had less influence (force) then slower wind would have more, and no wind would have the most. that makes no sense.
but on to the question. the answer is that the speed of the balloon horizontally asymptotically approaches the speed of the wind. think of it this way, there is some relationship between windspeed and force on the parachute, in so much as when the speed increases, the force does too, and when the speed decreases, the force does, too. in fact the relationship is that Force = Const*Speed^2, we just dont know what that constant is, just that it is positive.
so. we have that relationship and your starting point. a parachute with 0 velocity (in the horizontal, we're just gonna work there) and a large windspeed, relative to the parachute. that means the force is high to begin with, and the parachute accelerates in the same direction as the wind is blowing. but now the relative windspeed is lower, so the force decreases, and this keeps happening. the parachut keeps going faster and faster in the direction of the wind, but the force reduces, and so does the acceleration, until the force is nearly 0 because the parachute is moving at almost the speed of the wind.