There are several SmartSet clock Radios by Emerson. Which model do you have?
It's possible that you have alarm 1 and alarm 2 both set for weekends (if a two-alarm version). For the SmartSet radio, CKD5811, that I am used to, you can change the alarm mode between Everyday, Weekdays and Weekends. Press and hold the Alarm 1 (or Alarm 2) button then press the Alarm Mode button to toggle between the modes. Then release both buttons. If you press the Alarm 1 button, you will see the current alarm mode indicated by the indicators by the day that are lit. The Alarm Mode button is between the On/Off button and the Alarm 1 and 2 buttons on the CKD5811. Make sure that you have the Wake to Radio, Wake to Buzzer or Wake to CD slide set for the alarm in question. For Wake to Radio, set your station. For Wake to CD, make sure that the CD in the unit is one that actually plays in the unit (scratches, etc). Also check the volume (although that seems like less of a concern since it does wake you on weekends).
The manual for the CKD5811 is here: http://www.emersonradio.com/resources/owner_manuals/manual_1312917117.pdf
. Additional manuals are here: http://www.emersonradio.com/owner_manuals.php
. Scroll down in the drop down menu for the SmartSet manuals (clock radios all start CKD). The manuals are in alphabetical order.
I hope this helps.