Heathrow says the charges, which need to be approved by the Civil Aviation Authority (CAA), will help pay for £3 billion of investment, including the opening of the new Terminal 2 next year.
Airport bosses said that errors in previous passenger forecasts meant that Heathrow had lost out on around £650 million of charges over the last five years.
The CAA had based the previous level of charges on estimates that Heathrow would handle 78 million passengers a year by 2013, but the airport is only handling around 70 million.
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The painting, entitled 'Beautiful Beautiful George Michael Love Painting', was auctioned to help raise funds for HIV and Aids prevention.
The 38-year-old victim was standing on a busy Victoria Line train when another passenger approached him.
The boy, called Roman, told police call handler his mum "is dead" and "she's closing her eyes and not breathing".