I'm really sorry. maybe it's because I think this clause would be clear enough in itself for native English speakers so....
okay let me explain this
this clause is from 'The Landlady' ,one of the story in Roald Dahl's 'Tales of the Unexpected',
and The boy in the story named Billy Weaver is showing his wonder about how long ago
the last person came to this boarding-house so the landlady replies
'Dear me,' she said, shaking her head and heaving a dainty little sigh. 'I would never have thought it. How time does fly away from us all, doesn't it, Mr.Wilkins?'
The standard and clichéd way to sigh is to "heave a hearty sigh". This is alluded to in this expression but since the woman referred to is thought to be ladylike she heaves a dainty little sigh as that is the sort of person she is.