1.
considerably, to a great extent, very much
Indicates that something is to a much greater degree than expected or normal.
余程疲れていたらしい。
It seems they were considerably tired.
余程のことがない限り休まない。
I don't take time off unless something really serious happens.
あの人は余程自信があるのだろう。
That person must have a great deal of confidence.
2.
almost, nearly, on the verge of
Indicates that one nearly did something or was very close to a certain action or state.
余程断ろうかと思った。
I nearly turned it down.
余程帰ろうかと思ったが、最後まで残った。
I almost went home, but I stayed until the end.
あまりにも失礼で、余程怒ろうかと思ったが我慢した。
It was so rude that I nearly got angry, but I held back.
余程 emphasizes that something is to a considerably greater degree than expected. It carries a sense of surprise or emphasis about the extent of something.
SENSE 1 - CONSIDERABLY:
Indicates a high degree, often implying 'it must be quite...' or 'really very...'
- 余程疲れていた: was considerably tired
- 余程自信がある: has a great deal of confidence
- 余程のこと: something extraordinary
- 余程のことがない限り: unless something extraordinary happens
SENSE 2 - NEARLY:
Expresses that one was on the verge of doing something, often implying restraint.
- 余程〜ようかと思った: nearly did ~
VARIANT:
よっぽど is a more casual spoken form with identical meaning. 余程 and よほど are more neutral to slightly formal.