Ed is correct that the greater the lens focal length the stronger the tripod you need.
A small vibration in a lighter tripod will be more visible in a large print made with a longer lens (the longer lens has a smaller angle of view so the vibration effectively gets amplified and the more pixels you have and the larger the print the more the vibration will be visible).
Gitzo recommends their Series 2 tripods for 200mm lenses (300mm maximum) and the Series 3 for 300mm lenses (500mm maximum).
Generally heavier/sturdier is better but only as heavy as you will carry and use.
In a strong wind the lighter tripods will cause more vibration. Also if you use a 2x converter with your 200mm lens you would be at 400mm so the Series 3 would provide an additional margin. You can also hang some weight (your camera bag) from a hook at the bottom of the center of the tripod to get additional stability.
