Shed, HAL generates in excess of £1.6 BILLION of revenue a year from landing fees, passenger charges and navigation fees...that excludes ancillary income from car parking etc. build a third runway and increase traffic by 50%+ and they raise that revenue to almost £2.5 billion a year in today's money. That amount of revenue can support an enormous amount of capital borrowing, especially if you look at a 15-20 year payback.
You constantly compare R2 at Manchester with R3 (and T6) at Heathrow. They are not comparable projects and the latter will be funded by HAL not the taxpayer. I don't see you calling for MAG to pay for the SE Manchester relief road, or the work to improve the A556...you seem quite happy for the DfT to pick up the tab for those projects...
As for your sandwich analogy, perhaps look at it as HAL wanting to buy a sandwich but then their pals in TFL and the Lord Mayors Office and the local councils start dictating the fillings, adding a drink, crisps, nice lunch box to put it all in...that's how the price adds up.