Hi... If by 'weak heart' you mean being 'too emotional or worrisome', I won't categorize it as a problem but more of a preference in terms of one's personality type. Some people choose that as a preferred filter since childhood, while processing information in their surrounding or in their own thoughts and experiences. This occurs more when they have learnt it through a model (parent/elder sibling), who also uses the same filter. By the 'effect of learning', this preference takes shape of a personality type. But since it is learnt, in can also be unlearned. I will not suggest trying to change the complete personality to fit a particular template (internal/external), but to mold it in a manner that helps one grow in their own natural direction and be comfortable with their own self.
Next Steps
Find a good Therapist/Psychologist who can help you build your emotional skills.
Health Tips
Never get in conflict with who you are. Change occurs when we accept ourselves completely.