-times, round, game, revolve, counter for occurrences
回 centers on circular motion and repetition: something that revolves, goes around, or occurs in rounds. The counter sense is a natural extension of counting occurrences as cycles or turns.
回 is a pictograph of a spiral or revolving motion, with the modern form showing a smaller inner 口 inside a larger outer enclosure 囗, suggesting something turning within a boundary.
Picture a spinning top inside a box: the outer 囗 is the box, and the inner 口 is the top whirling around. Each spin is one round, one time, one occurrence.
For カイ, imagine a kite flying in circles: kite -> カイ, and each loop is one round.
counter for occurrences
this time; now
to turn; to rotate; to revolve; to spin
restoration; recovery; rehabilitation; return; improvement
previous time; last time; previous installment; previous instalment; previous session
rotation; revolution; turn; spin
every time; each round
collection; recovery; withdrawal; retrieval
reply; answer
first time; first innings; initial attempt
mawashi; belt; loincloth
number of times; frequency; count
evasion; avoidance
next time (occasion)
to turn; to rotate; to spin; to twist; to gyrate
circuit; line
to exceed (esp. figures: profits, unemployment rate, etc.); to surpass; to be more than; to be better than
circuit
event with ... rounds, innings, legs, etc.
going around; patrol; round; tour
withdrawal; retraction; revocation; repeal
return (to); revolution; recurrence
revolution; rotation; turning; circling; swiveling
putting off; postponing
recollection; retrospection; reflection; reminiscence
expression; phraseology
rotation
resurrection; resuscitation; coming back to life
one's personal belongings; one's vicinity; one's daily life; everyday necessities
to wield; to brandish; to flourish; to wave (about); to swing
corridor; gallery; hallway; cloister (i.e. covered walk typically circling a building or garden, esp. in a palace or place of worship)
recollecting; reminiscing; looking back; retrospection; review
to run around
interest; (investment) yield; profits
forwarding; sending on; redirecting (e.g. mail)
laying the groundwork; behind-the-scenes maneuvering; consensus-building process
to walk about; to walk around; to walk to and fro; to pace around; to wander
circulation (esp. of documents); sending round
role; part; job; assignment
recovery; rescue; recapture
one round; one turn; a circuit (of)
revival from the brink of death; recovering from a hopeless situation; resuscitation; revitalization
detour; circuitous route; diversion
rotation (of a post, role, etc.); taking turns
to run around; to bustle about
giant slalom
to search about for; to hunt around for; to look high and low for; to look everywhere for
to drive (a car) around; to ride (a bicycle) around
once; one time; one round; one game; one bout; one heat; one inning
three times
twice
how many times
death anniversary; anniversary of a person's death
coupon tickets; discount tickets; book of tickets
nth time
memoirs; reminiscences
several times; a few times