A TV show of the 80s assumed that a burger was the apogee of western sophistication. Today a "burger" refers to any westernised Pakistani (like me ?) in a derisory but humourous manner.
Devraj also cites a GupShup web forum thread that discusses the differences among the terms burger, abcd, mommy/daddy, tapori, anglo, tommy, paindoo, and more. The forum participants variously use the spellings "burgher", "burg(h)er", "burger" and "burghar", indicating some etymological uncertainty. In particular, there's an obvious connection to burgher in the sense "A comfortable or complacent member of the middle class" with burger the characteristically American sandwich, perhaps with some residue of a special Sri Lankan sense of burgher, glossed in Hobson Jobson as follows:
The Dutch admitted people of mixt descent to a kind of citizenship, and these people were distinguished by this name from pure natives. The word now indicates any persons who claim to be of partly European descent, and is used in the same sense as 'halfcaste' and 'Eurasian' in India Proper.
Devraj adds that burger-wannabes are known as bun kebabs "after the cheap, street version of the burger", and links to an article at Chowk by Ayesha Hoda Ahmad that presents this conversation:
Posted by Mark Liberman at June 13, 2005 07:42 AM
At a party, after two people were introduced:
First: “I live in Defence. Where do you live?”
Second: “I live in Gulistan-e-Jauhar.”
First: “What? Don’t mind but that’s a terrible place and you look the elite, you know, burger-sort.”
Second: “I used to live in Defence when I was young.”
First: “Oh, that’s why!”
The second one thinks, “So, does the shifting turn the burger into a bun kebab?