When you sweep the delay time, you get a momentary pitch shift. For instance, if you’re telling the delay to be shorter, you’re telling the delayed signal to happen sooner. That means that the waveform has to be shortened, and the peaks and valleys of the waveform get pushed closer together until the delay time catches up to where you want it to be. So you get a temporary rise in pitch. If you sweep the delay time back and forth, that’s the how a chorus effect is made.
Compare that to actual doubling of the signal, where there is a random difference in the attack time of a note, but the waveform is unchanged.