Too skinny to shoot!

Reduced loads. I'll probably never have a brake on a non-magnum caliber again. Even then, short of .338 Lapua I'd probably just put a HEAVY barrel on it. I hate the noise and blast.

If you really want to, change to a smaller caliber.
 
My daughter is a skinny little 14 year old and her rifle of choice is a Model 70 Featherweight, in .308. Her second time shooting it, we bought her a Past Field Shield and she's claimed the rifle ever since. A $20.00 solution and it worked for us. If she is really recoil sensitive, there is a $30 Magnum version available.
 
I weigh 100lbs and shoot a 7mm-08 Tikka T3 Hunter and modified the rifle to have the appropriate length stock, added a limbsaver and put a scope with longer eye relief. Having a rifle built to your size makes ALL the difference. I have an AR (I know this is the bolt action forum) in 308 and can only shoot with a Magpul ACS adjustable stock, I shoot the fixed Armalite stock and take a beating. Just bringing it up to re-remphasize that you need the rifle built for you - you don't have to change the caliber to something she considers wimpy (I know the feeling - show up to a shoot and have people ask you if you are big enough to shoot a big ol' rifle). Yes I am because it's modified to fit me!! :)
 
A 243 has a certain amount of " snap" to it also. It's got a fair amount if snappy recoil. Make sure you add a brake to a 243 or whatever she shoots. The brake will solve more recoil than a caliber choice.