A lot will come down to local knowledge of the airports and the way they tend to fog out. If I was confident that the alternate was not likely to deteriorate further I would be happy to proceed there. If I didn’t have sufficient knowledge I would have a rock solid alternate up my sleeve.
In my experience forecasters are not able to forecast with sufficient accuracy whether the vis is going to drop to 400m or 40m and it only takes very small changes in the atmosphere to get either of those readings. Once I start seeing low dew point splits and light winds at this time of year in NW Europe, I start to become very conservative in my fuel planning.