Rocket balloon hybrid

Picture a space ship inside a balloon. The shape of the outer balloon would be long and aerodynamic. The balloon would be a hot air balloon heated by the spaceship. The inner spaceship would be housed in a long tube of blast resistant material. As the main engine is used the inner rocket would travel up the tube to some extent to maintain equilibrium perhaps with some kind of spring loaded restraint.

The hot air balloon would be kept as near as possible to neutral buoyancy with the main engine performing acceleration. The buoyancy could be adjusted based on wind and external atmospheric conditions. The result would be that less of the thrust would have to fight gravity and more of it can be used to achieve acceleration. Once out of atmosphere there would be no need to jettison the outer balloon. Perhaps it should be closed at some point retaining some air and it may be that the outer balloon would be helpful for reentry as well.