So operator (TUI) mis calculate estimated weight. Clearly nothing to do with the aircraft.
Surprised this classifies as a serious incident.
If the weight estimate is too low, then it would be possible for the ground crew to load too little fuel, leading to a situation at the destination of nearly or actually running out of fuel.
So it may have been labeled "serious" due to the possibility of not loading enough fuel if the weight estimates are too low by too much.
For example if the aeroplane had been on a relatively short runway, and its passengers consisted entirely of overweight women who were miss-classified as much lighter children, perhaps it would have struggled to clear the runway at calculated power.
Flight crews are not trained to attempt to overrule the computer by explicitly commanding maximum thrust because humans are bad at figuring out if they're accelerating as much as expected - and so in the absence of a check that the plane is performing as anticipated † they are going to have a bad time if the calculations are badly enough wrong.
Why not just always use maximum thrust? Well if you're an aircraft carrier, or maybe even a military base you could definitely do that, but if you're a civilian airfield then the tremendous noise from jet engines at maximum performance is a constant problem and so you want jets to calculate a lower take off power that's still safe in order to reduce noise.
† [in some newer Airbus configurations the plane can work out its real acceleration and which runway you're on and conclude whether it will not successfully take off before it runs out of runway and so caution the pilots to abort before V1 when it's still practical - it doesn't matter why it isn't accelerating what matters is that you won't fly if you don't go fast enough, they can spend as long as they like to troubleshoot when they have stopped]
> As part of the prestart procedure, the flight crew reviewed the flight plan, which gave an expected takeoff weight (TOW) of 66,495 kg (Figure 1), and the load sheet, which gave a TOW of 64,889 kg (Figure 2). They noticed that there was a discrepancy, with the load sheet showing 1,606 kg less than the flight plan. They noted that the number of children shown on the load sheet was higher than expected, at 65, compared to the 29 which were expected on the flight plan. The commander recalled thinking that the number was high but plausible; he had experienced changing loads on the run-up to the temporary grounding as passengers cancelled and altered trips at short notice.
And...
"Whilst an incorrect takeoff weight was used for aircraft performance planning, the thrust required for the actual TOW and environmental conditions (88.2% N1) was marginally less than the thrust used for the takeoff (88.3% N1). This meant the safe operation of the aircraft was not compromised."
So it was a "something bad could have happened" situation that called for a change in procedure to avoid a future, real problem.
While my armchair opinion is that ~1500kg mis-calculation of payload on a Boeing 737 is minor - this is one of those problems you should treat pretty seriously as it might have repercussions on other flights.