Last time I read about that, the problem seemed to be buckling [1]. E.g. if you look at Euler's critical load [2] then the pressure that a slender column can withstand just depends on the aspect ratio of the column (imagine a vacuum airship that uses internal columns to withstand the air pressure). So scaling things up means, that the column's weight has to scale proportionally with total airship volume (and the (air) pressure is a constant anyways). See also these discussions here [3]. Disclaimer: I don't claim to understand any of this.
[1] https://en.wikipedia.org/wiki/Buckling