“Sammy” is a ludicrous nickname for a big (6’4 and a half, IMDb tells me), full-grown, badass demon hunter. As Sam points out in the pilot, it's a child's nickname. Twice in season one, we see Sam telling Dean not to call him by that nickname, but Dean ignores him. Sam eventually gives up, and we never see him objecting to John calling him "Sammy". In early S2, Sam declared "Sammy" to be a nickname that only Dean could use, not people outside the family. This changed as the seasons progressed - he tolerated it from Ruby, and eventually someone like Cole.
I don't think we ever hear Bobby call Sam "Sammy".
Two uses of "Sammy" by Dean, both during the Benny storyline, stick out to me: Dean's mocking comment about "Sammy's greatest hits" while possessed in Southern Comfort, and his appeal to Sam's affection while defending Benny in Citizen Fang.
"Sammy's greatest hits" is belittling and contemptuous. Using a child's nickname in that context implies that Sam is not taking responsibility for his "choices" - shades of "not man[ning] up". Dean had reacted to Sam's insistence on abandoning the nickname as if it were a pretentious affectation, but the thoughts and feelings brought out by the possession imply that Dean has issues with the nickname.
Demon Dean's attitude seems to be similar. I actually heard someone argue that demon Dean's repeated use of the nickname was evidence of demon Dean still having affection for Sam, but if anything it's a mockery of that affection.
But there is an affectionate side to the nickname. Dean's quiet greeting to Sam upon his return from the dead in Lazarus Rising ("Heya, Sammy"), is one of the most touching moments on the show. Sam's face makes it clear that in this moment, all that he's hearing in that nickname is love.
Citizen Fang provides another interesting use of "Sammy" as affectionate. It's three episodes after Southern Comfort, and the focus is once again on Benny and the lingering issues between Sam and Dean. Dean appeals to a cold and angry Sam by saying, "I just need some time, Sammy." Over Martin's heated objections, Sam gives Dean his time.
"Sammy" here is not at all contemptuous or belittling. Dean makes some comments in Citizen Fang that seem so designed to insult Sam that one wonders if it was intentional, but this is not one of them. This is a genuine appeal to the love between them, their relationship, even their shared childhood. And it works.
One final little "Sammy"-related observation: In Hello, Cruel World, in the scene in the warehouse, Dean only refers to Sam as "Sammy" once. It's near the end of the scene, after Dean has already pressed Sam's injury and Lucifer is starting to flicker: "You got away. We got you out, Sammy."
Prior to that, Hallucifer had not referred to Sam as "Sammy" at all. Immediately after Dean says this, he refers to Sam as "Sammy" three times in a row, and then disappears in mid-sentence as Sam presses his injured hand.