I would add a footnote.
Makes means
compels. Then:
absence compels the heart to grow fonder.
The heart is in the objective case, as can be seen if a personal pronoun is substituted:
absence compels him to grow fonder. But
him is still considered to be the subject of the infinitive phrase
him to grow fonder.
Looking at it from a different angle, the core meaning of the sentence is
absence makes [compels] the heart. How or in what way does it compel the heart?
To grow fonder, which may be thought of as an infinitive phrase modifying
makes.