Help with backpropagation equations for a simple neural network with Sigmoid activation
The gradient is actually calculated w.r.t to the weights so that each neuron would have a different 'change in the weight' according to its previous weight. In other words, not all the 3 neurons in the hidden layer will be penalized with the same value because the initial weights at t=0 are different for these neurone. 

It is well explained here: https://mattmazur.com/2015/03/17/a-step-by-step-backpropagation-example/ 

I hope this short answer helped!