1. with greater eagerness, enthusiasm, or readiness; more readily or voluntarily
I would more willingly help if I had more time.
Eu ajudaria mais de bom grado se tivesse mais tempo.
2. with increased preference or willingness to do something
She more willingly accepted the new job offer than the previous one.
Ela aceitou a nova oferta de emprego mais de bom grado do que a anterior.