If you can SSH to your devices, this implies that the connection service is working. Please get the output from the following commands:
ps ax | grep weaved
grep proxy /etc/weaved/services/*.*
sudo netstat -apn | grep tcp | grep LISTEN
Did the web connections EVER work via weaved/remot3.it? A stock install of apache/nginx/lighttpd normally works fine with our service, but some people have set their server configurations so that the traffic coming from 127.0.0.1 (which is how the daemon communicates to your server) is blocked.