big:
This is used to mean senior or most important. The big school is Secondary School (as apposed to Primary school) or High School:
“Ah’m goin’ tae the big school in August.”
Big lassie is a child’s term of address to an older girl or young woman:
“Hey big lassie, gonnae gie’s ma baw back?” (baw->ball->football)
Big man is a friendly term of address used to someone the speaker regards as being taller than himself:
“Can Ah get a swatch at yer paper*, big man?”
*swatch at yer paper = can I have a wee look at your newspaper?
a Brit different 
So then I shouldn’t be offended when my boys call me “big mama”?
Brilliant – we refer to secondary school here as Big School as well.
Big man – used in same manner.
Big girl – hmmm, think it’s a bit risky to use that here.
I think this is very interesting. Rather opposite of here. I love your accent, but you knew that.
I pushed enter before hearing the end of that one. I think I might do a permanent link to this one. You said arse for me. I might just cry!
Sometimes you do this and it makes me realise that I might not even know what I’m saying. You have a way of bringing things to light. I hadn’t noticed that people didn’t say “big” like that here. Could we be any more foreign?!
Another example – Billy Connolly’s nickname of ‘Big Yin’.