He doesn't know about Hawkeye's wife or his 2.5 kids, but he does know that when his sister was in trouble, the archer had stepped in and bolstered her flagging resolve. That was enough for him and without thinking, he speeds to rescue the Avenger and the child he is shielding with only his body.
If this is what S.H.I.E.L.D. is really about he can get behind that, even die for it if necessary. But none of that registers until the bullets rip into his back.
The child is safe, Hawkeye is safe and that's all that matters to him.