"to give him the top brick off the chimney."

meaning: no effort would be too great to keep the object of affection pleased, satisfied, happy.

Rightio. Now it makes much more sense - I guess she understood it as such too, but just reversed things a bit, to mean that they expect to be kept happy, and satisfied at all costs.
Thanks for the explanation there RC :-)

Here some proposed modernisations:
'to give him the best tracks of their mp3 collection'
'to give him their top-level domain in the internet'
'to give him the last megabyte on their hard drive'