The typical airliner departure isn't anywhere near the runway limited weights. Departures on runway weight limited weight flights use a lot of the runway. The flight in question was probably very near, or at, the runway limited weight.
As pilot observers we listen to engine noise (level of thrust being used), intial acceleration (indication of weight or thrust being used), rotation point, and initial climb rate to estimate the weight of the a/c we're observing.
Just like the videos of the 'Vodka bomber' show certain flights are known to be heavy. UK to TRS from a 2100 meter runway would be worth watching or videoing. Maybe other videos of the same flight number, and the same passenger load, would show if this departure probably was, or wasn't, normal.