You might first appreciate this is an extreme hypothetical, by now, with the actual Higgs Mass at 125 GeV, near the origin of the masses, far below any of the interesting structure you are asking about.
The controlling feature of these BR plots is the fixed-sum nature of the modes contrasted: since the ratios must all together sum to 1, much of the action you observe is normally the consequence of another, competing, mode fluctuating wildly at that scale, and not necessarily the mode you are focussing on! So, then,
The ZZ mode is competing with the WW mode, which is rushing to the WW threshold at 160 GeV, where the Higgs decay is real Ws, unsuppressed by virtual W propagators. So, at 160, the WW mode triumphs and sucks the probability out of the entire picture, and the virtual ZZ mode has to dip, in response, like the fermion ones. But, then, at the ZZ threshold, 182 GeV, also real Zs become a possibility, so the ZZ mode option becomes competitive, again, and it "recovers", grabbing its share of total probability.
Yes, this is merely counting the interactions of the Higgs to the eaten goldstons. There must be a Bose symmetry enhancement of the factor of 2 to its square, a factor of 4, which I have not found a simple illustration of, yet. The apparent ratio there is 3:1, which jibes with the ratio of couplings squared, $\cos^4\theta_W$...
Back to 1. The Yukawa couplings of the Higgs to fermions stay put, while the effective couplings to the above competing gauge bosons grow bigger and bigger, sucking probability out of the total. The bigger competing participant modes such as $b\bar b$ are the biggest losers when the gauge bosons hit the jackpot.
Admittedly, a hand-wavey picture, but that's just it: it is a fixed-sum picture, and, unless you can naturally sum graphs in your head...
Here is a superior version of your picture, from the horse's mouth, with detail informing my point,