I'm not sure why you have a > sign in the wget syntax. It seems like you're mixing the syntax of two different kinds of commands.
This command make sense to me:
php filename.php > output.txt
And this command makes sense to me:
/usr/local/bin/wget -o /dev/null -O /dev/null http://broadcreek.web.aplus.net/weather.php
But I don't know what this means... or if it even works:
/usr/local/bin/wget -o http://broadcreek.web.aplus.net/weather.php > -O /dev/null
You can't really output to an output flag? If it works for you, great. But if you're having trouble getting two cron jobs to work, I'd look at the syntax first. My crontab has about two dozen cron jobs, one per row, so I know you can run more than one.
I guess the best thing to do is run the command on the command line so that wget works exactly the way you want it to... and then put the cron timer "0 2 *" in front to make it work inside crontab.