The Govt is talking about raising APD at Heathrow rather than decreasing it elsewhere because the Govt is still spending far more than it receives in tax revenue. Or to put it another way, the country is still broke and the Govt needs to pay for the current economic mess. You've all seen what happened to Greece in the last few years.
The debate about increasing or decreasing public spending is a separate issue for another forum, but for the time being, with Heathrow being far more in demand than current runway capacity and partly regarded as the airport for the wealthier sections of society, the Chancellor is is no mood to decrease taxes from those who are perceived to be able to afford to pay.