You are going to run into a lot of confusing information, because some people meter at 200 to ensure extra exposure in the shadows, while others meter at 200 in order to ensure highlight density with pulled development.
IMHO, it is better to approach the question in a different way:
1) Choose your development based on the contrast you want; and then
2) Choose your metering EI based on the development you have chosen, and whether you want to manipulate shadow or highlight density.
Read that post very carefully. You pick a film contrast based on the contrast in the scene and the contrast you want to achieve on paper. That tells you the development time. Once you have your development time, you will then achieve a particular film speed. The formal expression of this approach is BTZS, which you can read about in Phil Davis' book.
It's worth keeping in mind that a B&W negative is basically not going to suffer in any way whatsoever for a 1-stop over-exposure. So you can expose it anywhere from 200 to 400, process it normally (as if it was 400) and get good prints from it. So in the common case, NO reduction in development is actually necessary when shooting at a lower EI.
Usually people shoot at lower EIs because the contrast of the scene mandates a reduced development time. Say you have deep shadows and glinting highlights and want to maintain detail in both areas. Reducing development can help you get there (it has other side-effects but we'll ignore that) but the reduced development means that the film needs more exposure in order to not come out too thin and unprintable. For example, I sometimes shoot Pan-F (a contrasty ISO50 film) at about EI16 to EI25 because I like to reduce the contrast.
So I think you have the causality backwards in your head. Instead of thinking "I wish to shoot at 200, how long do I develop for?", the approach is usually "I need to reduce contrast this much, how much exposure do I need?"
The "I want this speed" approach is really only taken for pushing, e.g. because you don't have enough light / shutter speed / aperture to get the photo without pushing. Note that pushing to higher EIs doesn't magically increase the film speed, i.e. Tri-X "pushed to 1600" doesn't achieve ISO1600 sensitivity. What happens is that a mid-tone will still come out as a midtone, some shadow detail will be lost and highlight detail will become un-printably bright. So pushing generally works best in scenes of very narrow dynamic range.