Weakfish are far more line-shy than fluke. Of course it depends on water clarity, but most fluke will readily bite on a 40 pound mono leader.
For some examples:
This year I was jigging for weaks off Sayville (almost zero clarity) and I gave my girlfriend my light rod with a 20 pound flouro tip. I was using my medium rod with a 40 pound flouro tip. She was outfishing me 6 to 1 until I realized the problem and put on 20 pound tip. Then to save my masculinity I caught about two dozen fish for the day.
One trip to Moriches this year the water in the bay was crystal clear and I could see the bottom in 15 feet of water like I was looking through a window. We were actually watching fluke come up to our baits and lures. They would swim up to them and follow them but no strikes. I went to a rod with a 20 pound flouro tip and was into fish for the rest of the day.
You have to be ready to change for the fish and conditions.