This is an older series of posts, so it may have become a moot point for the original poster. However, I am surprised nobody brought up the Nikon 300mm F4 PF. I've had that lens for a few months now and am blown away by how well it performs. I tested it pretty thoroughly against a few others I was considering at the time, mainly Nikon 70-200 F2.8 and F4, as well as Tamron 70-200 F2.8 G2, and it blew them all out of the water. All tests were shot handheld in fairly dark conditions. Ok, those other lenses all had less reach, but they also weigh twice as much as this 755g lens that easily outperforms them. If low weight is your thing, the only real alternative is the Nikon 70-300, which looks like it's been fogged up when you compare shots side-by-side (did that - not kidding).
Now, 300mm is not long enough for me. I do lots of birding and also shoot other small animals. Since buying the 300 F4 PF, I have tested Nikon's TC-14 and TC-20, both in their latest incarnations, with this lens, and found an interesting effect: while the TC-14 shows slightly better optical performance than the TC-20, I still get better sharpness out of the 300mm lens without TC, versus using the TC-14, if enlarging the shot in Photoshop accordingly. That is not the case with the TC-20 - sharpness is better with the TC.
On my D500, the 300mm plus TC-20 is a combination that's nearly impossible to beat: at an effective focal length (35mm equiv.) of 900mm, I can still shoot handheld at 1/30s and get tack-sharp pictures. Camera plus lens plus TC together come in about four pounds, still less than the 200-500mm WITHOUT camera. Not an overly cheap combo, but for far less than most serious wildlife lenses run, I feel this is a real keeper and highly recommend it.