か弱い、過去たち、過ぎる。

Was just singing "愛燦燦" in my head and thought I'd had an epiphany—that the か ka in か弱い kayowai, very weak, might be the same か as in 過去たち kakotachi, (things of) the past—both meaning "passing/surpassing(ly)", as in 過ぎる sugiru, to be too much / excessively (something). As in this poem that I have up at work (in calligraphy):

時過ぎて (toki sugite / time passes)
いつものように (itsumo no you ni / as always)
櫻さく (sakura saku / the sakura bloom)

So is it the same か? The Windows IME I type with, which takes input in kana and guesses at the kanji you mean, didn't replace that か with 過. Of course, it could be just a question of usage, like 時 vs とき； also possible that a connection was there at some point but is lost now.

不思議なものですね。

Addendum: Per Kotoba, sugiru and that ka are indeed the same.