He sold his Firecrackers and his service as bridge guard in exchange for his son Robert receiving the Senpou Monks’ treatment with Rejuvenating Waters.

Evidence

Robert’s Firecrackers have the following description:

Sold by little Robert and his father to raise funds for their travels.

Their voyage brought them to Japan, where they would seek the “Undying” in an attempt to extend Robert’s life.

Relatedly, the Ninth Prayer Necklace mentions that

Robert’s father came from afar across seas to the south, in search of the Undying. Repelling a thousand blades was a small price for the blessing of rejuvenation…

Undying suggests Senpou Temple, which lines up with the Warrior mentioning the Rejuvenating Waters:
At the start of the fight, he asks you to put down the sword “for the sake of [his] son”. If he kills you, he asserts that “[his] son will receive the Waters.”

Furthermore, the Warrior’s presence and the presence of firearms in Ashina aligns with the historical occurrence of Portuguese travellers arriving in Japan. Hence, it would be possible that he’s Portuguese, innwhich case it makes sense that the English “Robert” would be “Roberto” in his native language.

His death, his failure to guard the bridge, means that he will not just never get to see his son again, he may also fear that failure to uphold his end of the bargain will mean that his son will not receive the Waters, so their entire journey and all his effort, even his death, are in vain.

Given that evidently only one child survived the treatment, it’s quite possible that his efforts were in vain anyway, but he doesn’t know that. He only knows the terrible sting of failure to protect the one he cares about most, a sting that stretches over the seconds it takes for him to reach the ground.

And so he falls into his own personal hell. As the Temple flies away, so do his dreams slip his grasp. His last thoughts go to his young son, orphaned and alone, in a foreign land. He cries out in anguish, not for himself, but for the child he leaves behind.

I believe it was the knights son.