You would absolutely be fine with the medium duty cutter, the Woods 600 would be great for your tractor. It is still a very well built and durable cutter that will last you a lifetime. My tractor weighs 6k lbs with FEL and ballast in the rear tires, I use a 6' 1,100 lb rotary cutter (a true medium duty cutter, "heavy duty" to some). I handle the weight just fine as long as the FEL stays on. Without it I can do power wheelies relatively easy. A true heavy duty 6' cutter is too much for my tractor, I'm referring to cutter's like the Brown 672.
I have 39-40 PTO hp, it takes a bit to get the cutter spinning, but once there is great. If I do anything thick, like 2" material or more, I have to go very slow, it will overwhelm the cutter.
I've had both light duty and medium duty, I will never recommend a light duty cutter to anyone, not even for field mowing unless it's a very small tractor. There are times you can get away with Light Duty when all your mowing is grass and very small brush, but I would never recommend one. Not to mention, resale is horrible on light duty equipment, mostly because it's always pretzeled up and bent and torn apart.
Lastly, be careful on other manufacturers "naming" of they're cutters. You will see some advertised as heavy duty, yet, they weigh 500lbs with a 35hp gearbox rating.