An aerostat requires tethers
Which means that you now have a semi-unpredictable obstruction from 0ft to 60000ft that cannot easily be seen by pilots of other aircraft. You can map it out on a chart, but then you'll have to say "obstruction from point a with a potential circumference of xx miles" since it will never point straight up but bend in a curve. It will also have to go through various classes of airspace, including class A.
I'm quite sure that the average folks on the flight deck of your 737/A320 do not expect any obstacles when cruising at 35000ft.
It's just a bad idea.