I’m an undergraduate student and want to become an environmental economist. Would it be beneficial to take a class on weather and climate change or should I stick with economics courses geared towards the environment?
It wouldn't be detrimental by any means, but I would regard it as non-essential.
non-essential, because you'll likely use quite a simplified (as opposed to simple) framework for thinking about interactions between the economy and the environment. See for example Golosov et al. (2011) https://www.nber.org/papers/w17348
and non-essential because the larger models with more complex interactions between the economy and the climate/weather systems, would normally be conducted alongside some climate scientists. The division of labour here is arguably preferable, given that climate scientists and economists bring their own respective strengths to the table. I believe this to be the case in some of the integrated assessment models (IAMs) such as RICE/DICE etc.
But overall, if you believe it to be beneficial to your cause; I don't think it would be detrimental. Certainly it would enrich any modelling you'd consider doing.
[Seldom] give unguarded advice, for advice is a dangerous gift, even from the wise to the wise, and all courses may run ill. (Tolkien, the Fellowship of the Ring)
Let me offer a slightly different perspective than EB3112.
First of all you talk about "economics courses geared towards the environment" as your other option. As we don't know how much environment these courses contain it is hard for us to judge how useful the weather and climate course is relative to the other courses.
Second it depends on what kind of environmental economist you hope to become. Although many environmental economists work on climate change, by no means all of them do. For renewable resources a course in ecology may be far more useful, if you intend to work on pollution environmental science may be the way to go. Moreover, if climate change is your interest a course that focuses on climate science is probably more useful as weather and climate are very different beasts. Then again we don't know what your options are.
Although EB3112 is right that many EE models have either a very simplified version of the environment or you work with environmental scientists that do their part of the model, it is very helpful if you speak each other's language. This is especially true when setting up joint projects. For that such introduction to.... courses are very helpful. Also it prevents you from making mistakes in assumptions about the environment and how to correctly measure things in there.