When would bias regularisation and activation regularisation be necessary?

Regularizer's are used as a means to combat over fitting.They essentially create a cost function penalty which tries to prevent quantities from becoming to large. I have primarily used kernel regularizers. First I try to control over fitting using dropout layers. If that does not do the job or leads to poor training accuracy I try the Kernel regularizer. I usually stop at that point. I think activity regularization would be my next option to prevent outputs from becoming to large. I suspect weight regularization effectively can pretty much achieve the same result.