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This is what's happening: it's still between 8 AM and 5 PM on the weekend, so it locks it. Since you use an else if, it terminates the if statement and never checks the day between 8 and 5. I'm almost positive that if you checked it another time in the day, it'd be "unlocked."

Fixed code:

#include <Time.h>
#define doorPin 9
void setup() {
  // put your setup code here, to run once:
  pinMode(doorPin, OUTPUT); // Connected to relay to activate the door lock
  setTime(10,1,1,6,7,2014);
}

void loop() {
if ((hour()>=8 && hour()<=17) && !(weekday()==1 || weekday()==7)){
  digitalWrite(doorPin, HIGH);
}
else {
  digitalWrite(doorPin, LOW);
}

Note: ! means "not." Thus, the door is locked only if it's not a weekend and it's between 8 and 5.

Additionally, you might want to get a lock that is the other way around: unlocked only with power applied so someone can't unplug the Arduino to get access.