Hi,
it looks like beats just added the ability to enable gzip compression of JSON payload in this pull request:
This should be included in the upcoming 5.0 release then. It also seems you need to enable http compression on the ES side by setting the "http.compression" parameter on all you nodes, and this thread also suggests your response might be compressed in that case. Some things to try out, but at least this seems to be possible somehow in the neat future.