SMILE
with regards to your bieber reference, my friends call me bieber (a taller blonde version) hell ive even had girls come up to me saying lets get a photo with bieber and yet i consider myself alpha.
being alpha doesnt mean you are the most dominant man, it doesnt mean you can beat up every guy in the room, maybe long ago when we hunted and tribes kings were based on strength but in the 21st century this isnt relevant anymore, sure having a physical presence is a good thing but its not everything.
leading your interactions, being the decision maker, the one people turn to when they have a problem or cant make their own decision, thats being Alpha. you are the leader of the group or interaction through respect or social skills not fear.
and smiling doesnt show weakness it shows confidence, you are sure of your self and therefor your body language should be open and confident.