i think i'm in the minority here. while i sympathize with the girl's problem (i too was an overweight throughout my childhood-until i hit college) i see the issue as being the child both forged a note and then lied to the teacher when questioned about it. that is very serious in my opinion. in my experience this is NOT something kids "just do". it is a rather complex thought process that goes in deciding to deal with a problem in this manner (most girls would feign illness and try to get sent to the nurse or be allowed to sit out on the bench).
it sounds to me like the girl is more upset that she got caught than anything.
while the teasing may/may not need to be addressed at the school (unless it's hostile, bullying or harassment they will likely counsel the girl to avoid the boy and understand that teasing does occur), my concern would be to address what the girl had done.
i would take the girl personaly for a face to face with the teacher to confess and be supportive in whatever punishment the school enacts.
it may not seem like a big thing-but in reality what has occured is identity theft and forgery. i would want to question my child to make sure this is the first time she has ever done this and discuss with her the seriousness of the action.
having delt with forged documents and the persons who forged them (some children) i learned that the first time is the hardest/scariest-subsequent times become easier. many kids who have done it repeatedly will report that they did'nt get into "much trouble" for it the first time or two-so they continued to occasionaly do it figuring they would'nt get caught every time so it balanced out the risk.
best wishes to the op and her dd.
it sounds to me like the girl is more upset that she got caught than anything.
while the teasing may/may not need to be addressed at the school (unless it's hostile, bullying or harassment they will likely counsel the girl to avoid the boy and understand that teasing does occur), my concern would be to address what the girl had done.
i would take the girl personaly for a face to face with the teacher to confess and be supportive in whatever punishment the school enacts.
it may not seem like a big thing-but in reality what has occured is identity theft and forgery. i would want to question my child to make sure this is the first time she has ever done this and discuss with her the seriousness of the action.
having delt with forged documents and the persons who forged them (some children) i learned that the first time is the hardest/scariest-subsequent times become easier. many kids who have done it repeatedly will report that they did'nt get into "much trouble" for it the first time or two-so they continued to occasionaly do it figuring they would'nt get caught every time so it balanced out the risk.
best wishes to the op and her dd.
I've even turned into a fairly decent, ethical adult. 

Being Pooh sized myself and having a DD, now 19, who's generously proportioned, I've been there and think your actions have been completely appropriate.