I am in no doubt that referees are influenced by the stature of the the six clubs. I don't think they deliberately give decisions in their favour but I believe they hesitate to give decisions against them.
There's a lot of truth in that. Sir Alex Ferguson definitely tried to influence referees by his actions; such was his prestige in football that he was able to get away with things most managers wouldn't. One referee - it may have been David Ellary, but I'm not 100% sure - said in his book that there was tremendous pressure on refs from certain clubs, with fans in some cases finding out referees' home addresses and sending them hate mail. It's clear that Liverpool are similarly "favoured", partly because there are so many former Liverpool players in the media.
Look at last season - we got a clear penalty at Anfield in the league (Our first since Tommy Lawton's days); thanks to Klopp's antics and the ex RS media mafia, that was deemed "controversial", and we all knew that the RS would get a soft pen against us in the cup match, which duly happened.
Referees don't knowingly go out to favour certain clubs, but the unconscious bias is clearly there.