I need to just gush about Ed and Eddy and how emotional they make me for a second. I've talked before about how Eddy is the golden child in his family while his bro is the scapegoat, given the "#1 son" mug and his parents disapproval with him having anything to do with his brother. Well Ed's family has the same situation going on, with the youngest, Sarah, being the golden child, and Ed, the eldest, being the scapegoat. So you've got two best friends who have known each other since they were toddlers, one who was abused by his scapegoat big brother, and another who's currently being tormented by his golden child baby sister.
And that's not where the similarities end! Eddy and Sarah, other than being the youngest and the golden children, have a lot of other things in common, too. Their short tempers, violent outburts, permanent loud volume, and penchant for using Ed for their own gains make them shockingly similar characters. It's also pretty heavily implied throughout the series that Eddy is a mama's boy, and we have a pretty good idea of what Sarah and her mother's relationship is like ("I'm telling mom!")
So if they're that similar, why would Ed want to be around Eddy? The answer is the key difference between Sarah and Eddy; Eddy likes Ed, and Sarah does not (not on the surface, anyway.) Eddy will yell at Ed, hit Ed, use Ed, and be an all around asshole to the guy, but at the end of the day, he still wants to be around Ed. He wants to watch his scary sci-fi movies with him, pull pranks on the other kids with him, have sleepovers and camp out and encourage his overactive imagination. And Ed responds so well to this because Ed loves Sarah. And here's Eddy, so similar to her, and yet so different. Of course compared to how Sarah treats him Ed would see Eddy as soft and cuddly like mashed potatoes.
Then you have Ed, the scapegoat elder brother, twice Eddy's size and impossibly strong. If he wanted to, there would be nothing stopping Ed from ruling the cul-de-sac the way Eddy's brother supposedly did. We see in Little Ed Blue that even Sarah is scared of Ed when he's seriously angry, and he's easily the strongest kid in the neighborhood. It's Ed's own gentleness and loving nature that leaves him docile and so affectionate. I think that normally, Eddy would be scared of someone so much bigger and stronger than him, and that Ed probably does remind him of his brother in some ways. You'd also think Eddy would want nothing to do with someone as touchy feely as Ed is. And yet Eddy always seems to be having the most fun when he's joking around with Ed, even gets extremely touchy feely himself when the two of them are having a laugh together.
(btw the little giggle Eddy lets out before muffling his laughter by hiding his face in Ed's chest is the top cutest Eddy moment in the entire series.)
ANYWAY the point of me rambling about all of this is that I think Eddy and Ed see in each other the sibling relationship they wished they had, and through years of building their friendship, have created such a relationship. Eddy and Ed are brothers through and through, and it's why they remain so close despite the multitude of reasons they have for not liking each other.