TL:DR - The language has been carefully chosen to cast doubt on Rodolfo's adulthood and masculinity
Eddie is a traditional, older, blue collar dock worker with a conservative attitude to masculinity and the role of men in the family. Rodolfo, his wife's cousin, is the opposite. He is young, liberal and harbours wild dreams of a singing career.
Eddie has also developed an infatuation with his wife's young niece, Catherine. Rodolfo and Catherine develop a relationship and, eventually, begin dating. This further strains relations between the two men.
Here, Eddie's language is denigrating Rodolfo, trying to cast him as young, foolish and dangerously irresponsible. Furthermore, he is trying to convince himself that Rodolfo is homosexual. He is implying these things without saying them outright by his patronising choice of language.
looked so sweet there, like an angel – you could kiss him he was so sweet
"Sweet" is a description you might use for a cute child, not a young adult. This association is strengthened because sweets (as in the confection) are associated with children. You might also use it to describe a pretty young girl, casting doubt on Rodolfo's sexuality.
"An angel" is an interesting one because it is ostensibly a compliment on someone's virtue. But that is not the intention here, given the content. Angelic is, again, a phrase associated with the innocence of childhood and cherubim, literally angels in the form of a child. Innocence and virtue are also traditionally feminine qualities.
"Kiss him" is, coming from a man, another dig at Rodolfo's sexuality. This rough man is insinuating that Rodolfo is girlish enough in looks and behaviour to arouse sexual feeling in other men. It's also stated passively, suggesting that Rodolfo might actually encourage and enjoy such attention.
Paper Doll they call him. Blondie now.
"Paper Doll" is of course a children's toy, not something for a responsible adult. Furthermore it's a toy particularly associated with girls rather than boys, especially as they grow older. And paper is weak, easily torn, not like a tough man should be. There is a further implication on class and education here, since paper is associated on multiple levels with reading, writing and academia which, in Eddie's world view, should not be things of interest to a working man.
"Blondie" is a feminine name with further feminine implications. Men should not be interested in the colour of their hair. Blonde is not a description usually applied to men, with something like fair-headed being used instead. Blonde women are associated with a stereotype of being ditzy, stupid and unreliable.