Nothing keeps it from growing too large. In fact, this is the problem that has several theoretical solutions. First, people may develop and use lightweight cli

Nothing keeps it from growing too large. In fact, this is the problem that has several theoretical solutions. First, people may develop and use lightweight clients. They will only store wallet and sign transactions, but will not store and verify the blockchain themselves. For instance, they may refer to some public service to figure out the current balance. Second, there is a possibility to develop a client which stores only the block headers and downloads only necessary blocks to validate particular transactions. Third, it is also possible to compress/discard old blocks that contain transactions with empty recipient addresses.