I've always taken that stress (and the song as a whole) as a surprised realization on Eva's part that maybe Peron really did love her for who she is and not just the political benefit that she gave him, contrasted with her feelings towards him being one of usefulness like all the men in Goodnight and Thank You. And even at this point she has a hard time believing it is genuine love (hence this section):
Why are you at my side?
How can I be, any use to you now?
Give me a chance, and I'll let you see how
Nothing has changed
She's still going back to the political nature of their relationship while he is behaving according to a more emotional one.