I agree with Blunderbuss.
I think you being a UF grad may help in pleading your case in terms of going to UF Law (you know the area, what they have to offer, and knowing this, UF is something you want) but I doubt they will get too excited about it.
Show weakness? This isn't a try out for the Special Forces or a CIA Interrogation. You have a compelling reason to want to go to UF and ultimately, after 1L grades/rank, I think that is what Adcoms look for.