Heartily

adv.joyful, energeticwarm

Meaning 1

With open warmth, enthusiasm, or vigorous enjoyment.

Reach for it when describing a welcome, laugh, meal, or action done with evident gusto

The hikers ate heartily after the long climb.

playful
with gusto
lively enjoyment makes the scene vivid
not when The phrase is too jaunty for solemn praise or a formal endorsement.
everyday
enthusiastically
visible excitement powers the action
not when Enthusiasm can be energetic without the warm sincerity conveyed by heartily.
warm
warmly
affection and friendliness shape the response
not when Warmly may be quiet and restrained rather than vigorous.
professional
vigorously
physical energy or force deserves emphasis
not when Vigorous action can feel aggressive and need not be friendly.

Sincerely and emphatically, especially in agreement or approval.

Reach for it when strengthening a statement of support without suggesting careful qualification

The board heartily endorsed the apprentices' proposal.

warm
wholeheartedly
complete personal commitment is the exact claim
not when Wholeheartedly is stronger and leaves less room for reservation.
professional
strongly
the degree of support should sound direct and measurable
not when Strongly can express opposition as readily as warm approval.
formal
sincerely
genuineness matters more than force
not when Sincerity alone does not show the emphatic energy of heartily.

laugh heartily
Even the conductor began to laugh heartily at the harmless mix-up.
eat heartily
Everyone began to eat heartily after bringing in the apple harvest.
heartily recommend
I heartily recommend the quieter riverside route.

The definition and the example on this page are written here. The dictionaries above ground which meaning is being described, not the wording.