I ussually offer to pay when I invite a girl for a date, some of them insist on paying half that's ok with me. I'm not there to start a war over a bill. But most of the time I pay for everything that's ordered on a meal. But I won't pay for her if later we go to the cinema for example.
When I'm invited for a date by a girl (which is rare but happens from time to time) both of us pay our things. It happened once when a girl insisted to pay for all the meal.
It's not the money but the people that are important in a date. The bills are ussually bearable for anyone so it's not a big issue.
Paying for a meal to a beautiful girl is a sympathy not an obligation.
"E ao imenso e possível oceano
Ensinam estas Quinas, que aqui vês,
Que o mar com fim será grego ou romano:
O mar sem fim é português."