Personally, at the first drill heading out into open ocean I will brief the crew on the weather forecast and what is expected for the first few days. If heavy weather is expected I put a written order outside the galley to make ready their living and work spaces. I make a point to talk to each watch about the weather and discuss the forecasts and weather maps we are receiving. This has served me well over the years.
As for the engineers having an interest in weather. I have one Chief who could care less and another who adamantly wants me to forward him the weather everyday. I’m not a closed book so whatever anyone wants to know, they’re welcome to it.
On the subject of questioning the old man. I remember being a third mate with a couple years under my keel leaving out of the English Channel headed westbound for the states in January. The captain decided to take a great circle, keeping us to the north for several days and there were two fairly substantial lows tracking across the North Atlantic but at a fairly mid latitude. I was not enthused looking at our route for the soon to be ass whooping we were going to take on our forward house container ship. I voiced my concern to the second mate who had a lot more Sea time than me and he made the point for the old mans decision. Stay on top of the low in the lower sea state and following winds. When I looked closer it made sense. I just didn’t know any better at the time but that is what more Sea time gets you. Experience. We still got beat up for a few days, but nowhere near what it could have been.