Ok, it works like this:
T1 - The nuclei give give away energy to the lattice around them, so hydrogen compounds relax fastest, with free water being later (i think). T1 relaxation is quite fast compared to T2, so in order to weight an image towards T1, the pulses are sent in really fast, so there isnt time for T2 to happen, meaning only T1 relaxation gives off a signal.
T2 - Nuclei give it to each other, slower than T1, so to weight an image towards T2 you emphasise the later signals recieved.
Hope this helps
GMC