Hi
Actually, no. If I'm reading it right, she's describing drinking. (I'm not familiar with her or her music, sorry)
"Wake up puddle eyed" would describe how you would wake up after a night of drinking.
"We'll be heroes on every bar stool" is about the stories you tell your friends when you are drinking
All of that together makes me think that this verse is about alcohol consumption. So for the line in question -
"Seeing double" is a common symptom of being drunk
"beats" means "is better than"
"seeing none of you" - the person isn't around, so the singer can't see them.
The whole line together means that the singer is drinking a lot of alcohol so that they won't miss the other person.