Normalization is a ubiquitous neuronal computation that is important for safeguarding stimulus selectivity. However, normalization strength has been found to vary greatly across neurons. Here, we show that the normalization of responses by neurons in the macaque middle temporal visual area (MT) is profoundly affected by the receptive field responsivity at each stimulus location. An intensity-weighted normalization model, in which intensity is defined as the product of stimulus contrast and a location-specific receptive field weight, explains most of the previously observed variability in normalization across neurons. It furthermore explains systematic changes in the semi-saturation contrast of contrast response functions at different receptive field locations. Finally, intensity-weighted normalization reveals that spontaneous activity can be viewed as unknown excitatory drive that has measurable intensity and contributes to normalization equivalently to experimental stimuli.