feelings, heart, yearn, miss someone, become attached to, bosom, breast, pocket
懐 centers on the inner emotional space of a person: the heart, feelings, and the act of holding something dear. The physical senses of bosom, breast, and pocket are concrete extensions of that same idea of an intimate inner container.
懐 combines 忄 (heart) with a phonetic component that historically represented carrying inside one's clothing, giving the idea of holding something close to the heart. The modern simplified right side is a compact arrangement of 十, ⺫, and 衣.
The heart radical 忄 on the left sits beside a right side that looks like a container with 衣 (clothing) at the bottom. Picture feelings and precious memories tucked inside the pocket of your heart.
For カイ, imagine a kind person opening their heart and saying 'Hi' to welcome you in: 'Hi' -> カイ, and that warm greeting makes you feel attached.
dear (old); fondly remembered; beloved; missed; nostalgic
inside the breast of one's clothing (esp. kimono); bosom; (breast) pocket
doubt; skepticism; scepticism; disbelief
to become attached (to); to take (to); to become affectionate (with); to be tamed; to get close (e.g. to someone emotionally); to become intimate (with)
one's pocket
reminiscence; nostalgia; thinking fondly of the past; recalling the old days
winning over; placation; gentle persuasion
friendly; affable; amiable; sociable; loving company; (animals) taking kindly to people
pocket watch
to yearn for (someone, something); to miss
one's long-cherished desire
amiable; affable; likable
pregnancy; conception
kaiseki; sophisticated traditional Japanese cuisine brought in courses
nostalgic song; golden oldie
conception; becoming pregnant; pregnancy
dear (old); good old; longed-for; classic; nostalgic
speaking about (one's thoughts, memories, etc.); relating (one's feelings, reminiscences, etc.); recollection; reminiscence
paper folded and tucked inside the front of one's kimono (esp. for use at the tea ceremony)
long-cherished hope