You could point out to any station staff that if you try any carry a
30kg canine you are liable to injury which will mean a lot of extra
work for them. You could suggest they carry the dog for you if they
insist, but I would doubt whether they already have a safety case for
such occasions.
Incidently I have been on the underground in the past with two people
and a full-grown rottweiler. The dog went down the escalators to the
Central Line at Holborn and up from the undeground at Waterloo without
problem.

Neill