Besides, They'll see how beautiful I am And be ashamed –
And the list goes on – the "besides" here can really be read as a sort of "in addition" or "also."
All that laughing and that eating well have paid off – the speaker here is framing himself as "beautiful."
Of course, though, this can also be looked at as a kind of realization on the part of the white people – as in, the speaker hasn't become beautiful over the course of the poem, but has rather been beautiful this whole time. It's just taken this long (too long) for everyone else to realize it.
And you know when something's been really obvious, and you fail to catch on, and then suddenly you realize it and feel pretty stupid and embarrassed? (We've all been there – it's OK.) That's where the "ashamed" part of this passage fits in.
The narrator's basically saying, "Hey white America, once you people wake up and realize that I've been your equal all along, you'll feel pretty foolish."
And he's right, isn't he? Though Hughes wrote this poem before the Civil Rights Movement, he did a good job of predicting the future. In the 21st century, we Americans are ashamed of our history of prejudice and intolerance.