As part of the research done at Web3 Foundation, we have recently open sourced an implementation and an accompanying paper (code here and write-up here) that allows more efficient light clients which can be used as part of bridges or in the browser. Please have a look!
In more detail, GRANDPA-based light client would require verifying hundreds of signatures for every justification. Using aggregation of BLS signatures, we could reduce this to verifying one signature against hundreds of public keys. In our solution linked above, we do not need to communicate either hundreds of public keys or hundreds of signatures.