Ok, to follow up: indeed this turned out to be weblogic problem. For those that use haproxy with weblogic (mine are version 12c) backends, to make this work You need to enable following things.
On weblogic,
choose domain --> Web applications --> enable checkbox [WebLogic Plugin Enabled]
apply the changes, now open
domain --> environment --> servers (do this for each server) --> general --> advanced --> set [WebLogic Plug-In Enabled] to yes
On the haproxy side, add to the backend this:
http-request add-header IS_SSL ssl
http-request add-header WL-Proxy-SSL true
http-request set-header IS_SSL ssl
http-request set-header WL-Proxy-SSL true
Now restart Your weblogic and enjoy the magic.
Thanks for pointing me in the right direction: lukastribus
Have a nice day!