What is the highest balloons possible in a chain? The BU60-1 balloon attained an altitude of 53.0 km (32.9 mi; 173,900 ft). 

Weather permitting, would a series of climbable balloons in a chain be able to be linked from the ground to that height of 53 km? 

To gain altitude each balloon must be gradually bigger.
At the bottom balloons would be made of more durable material.



I have found no record of this being done with higher tech weather balloons.
It would certainly be possible to construct a series of balloons that reached neutral buoyancy at different altitudes, so in that sense the answer is "yes".

I'm not sure whether there's necessarily any correlation between balloon size and altitude, except in that a given balloon will expand as it rises.