If such a system works out, it could provide more than a few benefits to SpaceX. As of 2018, SpaceX estimates a cost of $62 million to launch a Falcon 9 rocket with a first stage landing factored in. If it can reliably slow down and recover the upper stage with a relatively low-cost method like a balloon, it can both reduce its own expenses and make launches more attractive to customers. Throw in the eco-friendliness (there's no dead stage plummeting to Earth) and it could easily be worth attempting to use a balloon, however ludicrous the idea might sound at first blush.

Update: Musk has added a bit of extra context, noting that a balloon would drop the stage's ballistic coefficient (the ability to overcome air resistance) by "2 orders of magnitude" while preserving its shape "across all Mach regimes."