I have observed that there are definitely better times to post questions than others based on GIS.SE user patterns. Questions that are posted when many viewers are present and active are more likely to get good answers. Alternatively, good questions posted at "off times" often go stagnant and get lost in the archives. As this really is a global GIS community, it is difficult to track when peak times occur. Are there any hard-data showing peak times to post questions? Or, in other words, when should users post questions to "get the most bang for the buck"?
There is now some statistical evidence at Meta SE to back up that weekend posting makes no difference to the attention a question ends up getting: Do questions posted on the weekend get less attention?
My thoughts prior to reading that appear below, and I think will still generally apply.
I think the best time to post a question is when you have a good question to ask because the sooner it is posted the sooner it is seen by a potential answerer.
If you post when there are lots of people active then your question is competing for attention with many other questions, and each potential answerer will be reading many questions that they could contemplate providing an answer on.
On the other hand during the quiet time on weekends I think you will find that potential answerers have more time to think about and respond to the "meatier" questions because the incoming questions that would normally distract them slow down.
I have no figures to back this up but I think the longer a question is posted the more likely it is to receive a useful answer, irrespective of what time of day or day of week it was posted.
To get "bang for buck", I recommend posting ASAP and paying attention to the advice of Asking good Questions for GIS Stack Exchange?