Underpinning the "mother" theory, here is Marianne Koch, former actress, at a recent TV appearance in Germany:

I think Eastwood also said that the original explanation was just too long which is why he cut it down.
I can't remember Yojimbo but what was the samurai's motivation?

Eastwood says that the script did give him a clear motivation to help Marisol, but he preferred to keep it mysterious and came up with "I knew someone like you once and there was no one there to help".

If you're really curious as to why he helps the family out, it's because that's what Toshiro Mifune's character does in Yojimbo.
As for Lee Van Cleef playing two characters, so does Gian (the guy who played Ramon in Fistful) who also plays the indian in the second film. Several otheer actors are in all three films alongside Clint Eastwood. That's just Sergio Leone using what he has and who he knows. The budgets for these films were not 200 million dollars, they didn't have a lot of resources. And come on, the poncho.

Well, Sergio's "Man With No Name" films are supposed to be a trilogy in reverse order, right?
Wrong. The films are unrelated in storyline and all the characters are different. This is why VanCleef plays a good guy in
For a Few Dollars More
and "the" bad guy in
The Good, The Bad and The Ugly
.
My vote history link:
http://imdb.com/mymovies/list?l=5504773

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I was thinking along these lines.
Sometimes they get a movie from overseas, and the cast/crew/writers don't have the same viewpoint as H'wood; they don't feel the need to write "sympathetic characters" to serve as a "rooting interest." So the H'wood executives say,
we like it, but it just seems like two bad guys fighting. Make the Eastwood character more moral, or have him make some sacrifice to show he's the hero.
So they create a scene which shows him to be acting out of noble motives.
I presumed that this is what happened in
Casino Royale,
too there's a scene where Bond starts ranting about how millions of people will die if he doesn't act fast. He actually
overacts
if you ask me, to drive home the point that
Bond really is the hero, even though he seems cold-blooded.
(That scene just seemed like it was added at the last minute.)

I think maybe the scriptwriters just thought they needed to give a reasonable explanation for why Clint's character would stray from his usual opportunism and risk his ass to help someone else. That line of dialogue hinting at something personal and strongly emotive was probably thrown in out of sheer expedience. My guess is the scriptwriters never even thought of anything or anyone specific in way of a background story.
That said, the 'mother' explanation would be as good as any.

Yes,
I also always thought she reminded him of his mother, also seen the fact that much attention is based on Jesus (the kid) which might have reminded him of himself.
Thinking of it now, Leone was a huge fan of Kurosawa (Leone's style is actually an extension of Kurosawa's style) and there is a scene in The Seven Samurai where Kikuchiyo (Mifune) recognises himself in one of the children victim of a war
"
What if there is no tomorrow? there wasn't one today!
"

El sueo de la razn produce monstruos

I believe that he was talking about himself when he used to be a woman.

I believe that he was talking about himself.
"gonna throw, my raincoat in the rivergonna toss, my umbrella in the sea"Sammy Turner.