Balloon tanks, first used on the MX-774 sounding rocket (the direct, though distant, ancestor of the Atlas family of missiles and launchers), are structurally stabilised by internal gas pressure, allowing the rocket’s skin to carry the entire structural and aerodynamic load of launch and dispensing with the large, heavy stiffening ribs and longerons required by non-pressure-stabilised tanks. This, obviously, makes for a far lighter rocket, allowing a much larger payload to be carried to orbit (or, alternatively, allowing a much greater Δv to be imparted to a given payload). The only significant drawback is that the rocket’s propellant tankage must be kept pressurised at all times to prevent the rocket from collapsing under its own weight, but this requirement is easy to fulfill at any launch site equipped to launch liquid-fuelled rockets of any sort.
Yet, despite the tremendous weight savings, very few rocket designs have ever used balloon tanks; so far as I am aware, the only ones to have flown are the MX-774, the older members of the Atlas family (from the Atlas A missile prototype through the Atlas III space launcher, inclusive), and the Centaur upper stage (fitted to all Atlases since the mid-1960s, and still used today on the Atlas V; also formerly used as an upper stage for the Titan IIIE and Titan IV, proposed for use as an upper stage for the Saturn and Shuttle launchers, and planned for future use on the proposed Vulcan launch vehicle), and, of these, only the Centaur remains in production.
Why are balloon tanks seemingly so unpopular?