noun
past the middle; beyond the midpoint
Used for time, age, or progress that has passed the halfway point. Often implies a sense of being well into the latter half.
会議は半ば過ぎまで続いた。
The meeting continued past the halfway point.
彼は四十代の半ば過ぎだ。
He is past the middle of his forties.
半ば means 'middle' or 'halfway', while 半ば過ぎ specifically means 'past the middle'.
Compound of 半ば (middle) and 過ぎ (past, exceeding).