The Saturday afternoon extra hours (I think until about 5pm) is to offer the services which have in recent years developed to the Mediterranean etc with the weekdays business fleet. Opening between 7am and 1pm as currently on Saturdays just does not give a reliable round trip to the Mediterranean. There's a squadron departure as soon as it opens, but it's found just not reliable enough to be back in time before it closes, with diversions to Gatwick/Stansted or wherever, and for the longer round trips just not possible. Sundays it's not an issue, as it's open from 1pm to 10pm, a Med round trip followed by a Sunday evening outwards to a continental Business point, ready for an early inwards on Monday morning.
There was supposed to have been a local authority (Newham) consultation on this. We live closer than most, and heard absolutely nothing about any such consultation, though I'm sure John Stewart (does he still live in Twickenham ?) will be well to the fore in commenting. In passing, from my own consultations over time, none of our neighbours have any issue with the airport's hours at all.