It’s not really the weight, but the thickness of the meat that changes your cooking time (as you want a consistent level of doneness throughout the meat - thicker cuts take longer to get that temperature all the way to their core).
A REALLY good guide on thickness, using ice baths and so much more is here: http://www.douglasbaldwin.com/sous-vide.html
As for why the temperatures are different for rare, medium rare, etc - that really boils down (no pun intended) 
to personal bias. You’ll find med-rare is different from steak house X vs steak house Y. Same thing. The beautiful thing about sous vide is, you can play with that range around your desired level of doneness and decide what is absolutely perfect for you…and then repeat it perfectly every time you prepare them!!
When it comes to beef - the longer you cook it, the more tender it becomes. Fantastic information on just what that means for steak can be found on Serious Eats here: Sous Vide Steak Guide | The Food Lab
There is an immense amount of information on sous vide cooking available online…google is your friend.