…rushed to one side of the plane to see a volcano erupt ?
All the passengers mass would cause the plane to lurch to the left, while simultaneously their extra gravity would unbalance the delicate state of the volcano, causing it to erupt furiously! This would singe one of the plane’s engines. It stabilizes but unfortunately a flock of killer geese-bees smashes into an engine which leads to it exploding 5 seconds later. Half the plane is sucked out due to the resulting hole, while the other passengers are saved by some Transformers who just happened to be in the area.
In a universe not governed by Michael Bay, nothing happens.
But what if all the passengers were morbidly obese, AND members of the local Anvil Collectors Society, each with an anvil in their carry-on bags, which they just happened to be carrying with them, not properly stowed in the overhead compartments?
Would ACME industries have a safe, and expedient solution to their dilemma?
The french actor peeing on the floor could use the bathroom instead.
Serious answer: Not a lot. The moment arm is too short to have much of an effect.