The tower had held the weight of the top block just fine for decades, and the plane impact didn't increase that weight.
1. The weight was held by columns.
2. Some columns were damaged/destroyed by the impact.
3. Some columns and trusses were weakened from heat.
4. NIST showed that this reduced the load capacity of the structure so much that it failed.
5. The structure became unable to support the top block, because of 4.
6. The top block fell on a floor below, increasing its load.
7. The floor became overloaded, detached from the columns, and fell.
8. The debris fell onto the floor below that.
9. The floor became overloaded, detached from the columns, and fell.
10. The debris fell onto the floor below that.
11. The floor became overloaded, detached from the columns, and fell.
12. The debris fell onto the floor below that.
13. The floor became overloaded, detached from the columns, and fell.
14. The debris fell onto the floor below that.
15. Repeat all the way to the bottom.
This left the facade and much of the core standing, but unbraced, and the pertubations of the debris avalanche caused those columns to fall as well in short order.
tl;dr the impact & the fires destabilised the top block, the weight of the top block then overloaded the floors in turn.