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.
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
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.