I might say something controversial so be warned.
I think all that metering for birds in flight is nonsense. There are two factors that define everything; shutter and aperture. We don't have much choice when it comes to shutter since we want to freeze the bird. That forces us to use a pretty fast shutter depending upon the type of bird and how much of it we have framed. The aperture is defined by either the sharpness of our lens or the DOF we need.
So whatever the meter says; we are stuck with a certain shutter and aperture. It will rarely be overexposed and we can do little to get around that. All I do is make sure I freeze the bird and get as much light in as I can by opening as wide as possible. If I spot, center or matrix meter changes nothing.
Only during the rare occasions I overexpose, I up the speed or close down but that's once every blue moon for BIF.
Let me add something especially for dark birds vs bright surroundings.
They're hard to begin with but all we can do is maximize light using S/A. When we start upping the ISO, we increase the problem. There's very little detail gain in the darker parts and what we gain, we lose to noise. In case of the D7100 you gain about 1/3th stop DR in the shadows up to ISO 6400. If I'd use 800 to try and get more detail, I gain very little, pollute my signal because of amplification and blow the whole sky by now having 8 times as much light. And I still need to pull the shadows in post resulting in increasing the additional noise.
I don't use ISO but even if I would, I'd not gain anything by using more ISO than the shadow improvement it brings. It's better to use the minimum amount to get the maximum improvement and do the rest while processing. You end up with a cleaner signal thus less noise and don't blow all highlights. The meter will most likely tell you that you're underexposing but that's simply how it is. When you maxed A/S, you can't do much more regardless what the meter tells you.