I'm not all too sure if there is a definitive way of doing this if it's even at all possible, but, I might as well put in my two cents.
Looking at Sky Maker, on the Cycle tab, the maximum Time is 6999. I'm going to assume that that is the equivalent of 24 game hours, or for lack of a better word, from sunrise to sunrise, sunset to sunset, etc.
That may be where you do the math. Half of 6999 is 3499.5 (and since no other Maker in the game besides Object Maker allows for decimal values, you'll have to put just 3499). 3499 is the half-way point on the timeline in the Cycle tab, so what I would do is drag the scroll bar to that half-way point on the timeline, then choose your weather file and set the duration also to 3499, and click New Weather. What the game will do is add the weather cycle to start at the half-way point to the end. I have a couple of weather cycles that go as long as the 6999 limit, which they pretty much go on forever no matter what time of day it is in the game, so my logic is if the weather is set to go half that, it should only last during the night or the day.
However should this fail, my only other reasoning would be that because a sky file and a weather file are both separate files you'd put into Map Maker, there is no way to link the times up, they both move on their own and will happen when they happen.
Don't be discouraged tho, someone else might have a better answer than me, so keep trying until you get a definite yes or no.
