The right way is to specify both of those slashes. Slash after 127.0.0.1:9000 is essential, without it your request /elasticsearch/some/route would be passed as-is while with that slash it would be passed as /some/route. In nginx terms it means that you specified an URI after the backend name. That is, an URI prefix specified in a location directive (/elasticsearch/) stripped from an original URI (we having some/route at this stage) and an URI specified after the backend name (/) prepended to it resulting in / + some/route = /some/route. You can specify any path in a proxy_pass directive, for example, with proxy_pass http://127.0.0.1:9200/prefix/ that request would be passed to the backend as /prefix/some/route. Now if you understand all being said, you can see that specifying location /elasticsearch { ... } instead of location /elasticsearch/ { ... } would give you //some/route instead of /some/route. I'm not sure it is exactly the cause of your problem however configurations like
location /elasticsearch/ {
proxy_pass http://127.0.0.1:9200/;
}
are more correct.
Now may I ask you what you get with exactly this configuration in response to curl -i http://localhost:9200/ and curl -i http://localhost/? I want to see all the headers (of cause except those containing private information).