Priority
Rexy - There are lots of things that affect the priority of your baggage. If it is for arrivals at Heathrow, the biggest cause of timing is the way the plane was loaded for departure. All that BA baggage handlers do is unload the plane which should in theory have connecting bag containers unloaded first then First and Business Class arriving at Heathrow, then the economy bags.
What class were you travelling? If it was World Traveller for arrival and baggage collection at Heathrow this isn't the priority.
Remember whatever is loaded first will be unloaded last. So being one of the first to checkin won't help as your bag will be at the bottom of the container. Also, if your flight has multiple pickup stops the containers loaded at the 1st departure station will be unloaded last.
Bags are sorted by machine using the bar codes and just about every airport, they don't read the "priority" or "First" tags.
Bottom line - it depends, but it isn't something personal against you.