A fairly quick check on the longest (by non-wingspan measures) flying birds in the world suggests 2 m is very large. Admittedly, Argentavis, the heaviest known (if extinct) flying bird, was about 3.5 m in length, which counts its tail feathers. Still, with its claws, snout, teeth, and tail, this probably weighs more than an Argentavis. Quetzalcoatlus is bigger, but apparently there's been debate about whether and how it could fly, which is affected by weight estimates. That brings up the same issue.
Unfortunately, I will have to return later to this matter.