Haven't seen any Big Match re-runs recently but I do remember West Ham being on there almost every other week.
I know it was London Weekend Television so there was always a good chance of them being on but they did seem to have more than their fair share.
I suppose it may have been down to all their England internationals they had playing, including the late great Bobby Moore.

Funny what sticks in the mind though, for example Pat Holland.
I remember Brian Moore always referring to him as Patsy Holland.

Another I remember when Spurs played and had a throw-in, Moore would utter "Chivers with the long one"