Yeah, so even if you use the 50:50 weights (as suggested by Bobbybax), it's still a very asymmetric fly, which makes it a tough one. This is the long-term plot of the yield fly from BBG:
View attachment 182147
This is what the yield fly looks like long-term: View attachment 182148
I would find it difficult, here and now, to join the trend and be short ZN in that fly, given just how historically extreme it looks.
I'm an old school Eurodollar spreader. A fly is 1:2:1. He can use TN in place of ZN to have a better duration dispersion. If you decide to change the ratios, I'd recommend that you trade them as 2 separate spreads.