I grew up in Sale. When the winds were easterly, planes used to come over us after they took off. They were quite noisy on the climb out, especially back in the day of BAC 1-11 and Tridents. When winds were westerly, planes would fly over our garden then turn over Sale Water Point which is a VRP (visual reference point) then out towards Stockport. That has changed over the years.
For noise abatement, planes climb to a certain level quickly (3000 feet or so) then climb more slowly. So in the past, if one climbed steadily to 20000 feet and you lived 4 miles away, it would be much higher than now when it would be lower and climbing more gently. It put a lot less wear and tear on the engines and is less noisy for the residents.
At Heathrow, they vary the take-off and landing runways weekly and swap at 3pm unless they are using 09 (easterly winds) due to noise abatement. At Manchester, since the 2nd runway opened, then reopened after Covid, planes are going to be at a slightly different height and trajectory depending on which runway is in use.
When I lived in my last house in Exeter, we were 2 miles from the end of the runway. Our neighbours moaned like mad about the planes (ironically there were hardly any and even fewer now). The estate was built in the mid 90s - the airport opened in 1937. I loved it and often listened in to ATC on my scanner. One flight came in over our house but just as it was about to land, the Captain shouted "Going around". The ATC asked if everything was ok and the Captain explained that due to really heavy rain, he couldn't see the runway surface clearly and wanted to wait it out. He was advised that a clearer patch of weather was coming through shortly, asked about how much fuel he had, and sent 10 miles away to do some orbits at 4000 feet to wait for the clear slot. he landed safely 20 minutes later.