Scheduling wouldn’t be too hard. You could approach it a number of different ways:
1.) using the schedule command and cron tab settings you could indicate which days of the week (see more detail here: http://docs.codehaus.org/pages/viewpage.action?pageId=51488 and here: http://en.wikipedia.org/wiki/CRON_expression#CRON_expression)
2.) You could probably read the time/day some how (now command?)
3.) You could use different modes for weekday morning vs. weekend morning
4.) You could also conceivible set this up as a “run when tapped” app… something that schedule the ‘fade in’ to happen at 6:30am the next day only after you’ve tapped the app.
I think that option 3 and 4 might work the best for you. Yes, it does require that you do any extra step of either tapping the app or changing modes, but the nice thing here is that is also won’t automatically operate when you don’t want it it. For instance, let’s say you’re sick or have the day off tomorrow. Using either method 1 or 2 means you have to uninstall the app. But option 4 is simply change the mode to weekend morning. Option 3 is simply not tapping the app.
In a similar way if you need to get up early on a Saturday or Sunday, you can easily set the app to run those days with option 3 or 4. Options 1 or 2 means changing the code in your program.