a few months ago something must have changed in our network because after that I wasn't even unable to enter my FTP or MySQL server. Unfortunately all those things work with mobile internet, but I can't even login to my weaved account on my Raspberry Pi when I turn mobile internet, it just stucks at "Checking your network for compatibility...".
Here is the output of the commands you asked for:
pi@raspi1:~ $ cat /etc/os-release
PRETTY_NAME="Raspbian GNU/Linux 8 (jessie)"
pi@raspi1:~ $ sudo dpkg --status weavedconnectd
Status: install ok installed
Maintainer: Gary Worsham email@example.com
Depends: libc6 (>= 2.1), mawk (>= 1.0), net-tools (>= 1.60-24), grep (>= 2.1.6), curl (>= 7.25.0), psmisc (>= 22.19-1), cron (>= 3.0pl1-124)
Description: remot3.it provides private, secure connections to tcp services.
Use remot3.it to connect easily, privately, and securely to your networked
devices across the public Internet without port forwarding. remot3.it is
compatible with most devices that include a TCP/IP stack. The remot3.it
APIs and portal allow for easy 'bulk' management of multiple devices in
the field through a "one-to-many" command line interface.
See remot3.it for more details.
pi@raspi1:~ $ weavedconnectd.pi -n
WeavedConnectd built Apr 13 2016 at 16:56:27 Now Starting Up
Version 3.5 - (c)2016 Weaved, Inc. All Rights Reserved
Built with ALIGN BCASTER MALLOC_POOL LINUX RESOLVE BIGBUF NOTE pool=262144
Raspberry Pi Version
Running Weaved Network Diagnostics
Checking if DNS works ... .[OK]
Checking TCP connectivity to weaved.com... [OK]
Checking UDP connectivity to weaved.com...
Send to 126.96.36.199:5959  [mip=188.8.131.52] [oport=59612 mport=59612] [preserve port]
Send to 184.108.40.206:5960  [mip=220.127.116.11] [oport=59612 mport=59612] [no remap] [preserve port] [OK]
This router preserves ports, this is optimal.
This router doesn't remap new connections to new ports.
Static Pool Free
Endian : Little