Amplitude of Signals
Let's consider how k-space varies in the phase encoding direction first (from one acquired line to the next). Remember k-space is acquired (usually) in lines. The central line of k-space is acquired when there is no phase encoding applied, and very near the centre there is only a small amount of phase encoding applied. The phase encoding gradient, as well as encoding the signal, also causes dephasing. (But the spins are still close enough to the resonant frequency to give a signal. This dephasing simply refers to the fact that they don't add up to as much signal.) This means that at the top and bottom edges of k-space, where there is "stronger" phase encoding, the amplitudes of the signals are smaller than at the centre.
This isn't the whole story though, because across any one line of k-space (left to right), there is also a variation in amplitude of the signal, with the largest amplitude at the centre. As the echo is sampled, the gradient which is applied to encode the data in the frequency encoding (aka the "readout gradient") also causes dephasing. So both our essential gradients are working against us!
Remember that a dephasing lobe of the readout gradient is applied just before we read out the echo. If we left this part of the readout gradient out, and simply sampled the echo, the strongest part of the signal would be during the first few points in the line of k-space that we record, and the amplitude of the signal would decrease as we sampled points for the middle of k-space, and decrease even more for points in the last half the k-space line. This is not the best arrangement, because as you know, the most important part of k-space is the centre, which contains the low frequency information that determines the contrast in the image (as opposed to detail, edges and lines). (This is well illustrated in the k-space web tutorials on this site.) So what is the solution? We apply a dephasing gradient first, before reading out our echo. This means that the first part of our readout gradient reverses the effect of the dephasing we just introduced (as well as reading out the first half of the echo). In this way, the spins are in phase—giving a stronger signal—just when we want them to be: at the centre of k-space.