The choice of preposition will depend on the context.
Thus, especially when the forecast deals with a product, time or location, and when no specific amount or range is mentioned, you will probably choose for:
The (weather) forecast for the next week
The forecast for gold in the short term
The forecast for the cyclone season
The forecast for the country this weekend
On the other hand, when amounts, ranges or weather phenomena are concerned, of is more likely:
There's of forecast of five to six inches of rain this weekend
The forecast of gale-force winds...
The forecast of snow and sleet over a wide area...
In some contexts, both of and for are possible:
A forecast of/for a sunny weekend.....
Although we would speak of the forecast for global growth in general, in your example I would use the forecast of weak global growth, using of ahead of weak (or another modifier).
On the other hand, the forecast for weak global growth is perfectly acceptable too. It might depend on what follows or simply personal preference.
However, you cannot make fixed rules concerning the use of prepositions as the choice is governed largely by idiom.
Best Answer
If for = in support of seems "weird" in this context, try thinking of it as heading for, pointing in the direction of, as in "I'm for bed". But I think it's just as "intuitive" to see OP's example as short for...
Note that there's no real need for a preposition at all in OP's exact context, and semantically it's irrelevant whether it's sun or sunny (both are perfectly valid and commonly used).