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Since I never managed to grab that third stripe in rank, my view might be pretty useless to you, but here goes.
The USMC is BIG on leadership in all ranks, so its nudged, pushed, shoved and poked into you at every opportunity.

I have dealt with one of those, "WHY?" troops before, and found myself having a mental fantasy about taking a tire iron to their head while screaming at them "BECAUSE I SAID SO!" but you know how that goes... Anyway, what we did, when we had someone questioning orders, was to put THEM in charge of a small unit... say two or three troops assigned to a job, and give the "Why?" troop a list of what needed to occur during this job. Once they had to figure out why or how for themselves, while others questioned them, made them a lot more understanding when they finished, and if it didn't, Office Hours could be had for 'failure to comply."

I know, hardnosed way of dealing with it, but you spend half your day explaining things that are so simple in the first place that sometimes its necessary to let the fools sink to their own level, and the cream rise to the top.

He’s on profile. So have him walk around all day picking up trash and cigarette butts. I’d do it to embarrass him while his teammates are really in the Army. Hopefully he shuffling around in slippers or flip flops. You can’t smoke him or punch him in the face so I’d embarrass him to the best of my ability as a worthless shithead.

All your troops are different. Things will never be perfect or just like you want them. You've got to accept that and objectively assess whether your leadership style and methodology is effective. I suspect that since this guy doesn't like you, he will never allow any leadership style you employ to be effective where it concerns him. Don't ask questions that you don't already know the answer to. Let your subordinates know that first of all, we are going to do what the commander tells us to do. We will all follow the orders of the superior officers appointed above us. If someone thinks that they are not going to do these things then they'd better have a very good reason because counseling statements, corrective training and UCMJ action will follow. No need to get all emotional about it. It's just business as usual. They will either swing with you or swing against you. The ones who swing with you will be rewarded by enjoying a good reputation, positive counseling statements, selection for schools, advancement and awards where appropriate and a notable lack of UCMJ action. Speak to your PSG and get his opinion on the matter. If you work in conjunction with him to get this guy to either toe the line or leave the Army things will go more smoothly for you and be less frustrating. You can't save them all and that is not your job anyway. He may respond to the correct application of pressure and he may not. I wouldn't get worked up about it because there are a million more waiting to take his place. Above all set the example and be truthful.

Rank is just a promotion. You have to earn respect and trust. Bottom line you can no longer be their buddy. It is called leadership not management.

This is going to sound odd. When I was a sergeant, I never directed anyone to do push-ups except at PT. When....
- ...a Soldier forgot some item for a layout during an operational readiness survey, I had him spend that Friday night writing an essay about historical examples of disorganization and lack of discipline affecting the outcome of a battle. I had him show progress on the paper every hour on the hour to the Staff Duty NCO until complete.
- ...two Soldiers who demonstrated their ability to run 2 miles in NINE MINUTES (so, two four-minutes-and-change consecutive miles) on their APFT fell out of a six-mile easy ruck march, I had them meet me at 0600 that Saturday in front of battalion with rucks packed to TACSOP load-plan, and told them we would walk until we got a 12 mile movement in under 3 hours, no matter how many miles that took. (It took exactly 12 miles and maybe 2 1/2 hours.)
- and so forth.

I never had to correct the same problem twice.

First question I need to ask, are you active duty or National Guard? Huge difference in support you will get with your chain of command, and even bigger deciding factor on disciplinary solutions. I was both active duty Army first, then National Guard. When newly promoted SGT's on active duty were promoted unfortunately for them they were MOST LIKELY moved out of the unit. Not always but most of the time. That reduces fraternization among recent peers, also helps eliminate your very problem all together. I found it was tough to do that in the National Guard because of hardships it caused being that units are scattered long distances all across the state.

I will say, counsel the Soldier about it. Let him or her know what you expect. Let em know what you feel they are doing to you and the affects that is causing to the rest of the squad. Have a heart to heart if you have to. Try to put the shoe on the other foot. Ask him how they would handle a Soldier in which you describe. Perhaps go another route and put a lot of weight on their shoulders. Keep em busy and feeling empowered. If all else talk to your SSG or SFC, let them know what's going on and see if they can guide you. They most likely know the Soldier just as well and may give you the best advice. Or see if they can move him to another squad.

Best of luck either way.

Lock his heels, if he questions an order, snap his a$$ to attention and tell him “that’s a lawful order”. Tell him that if he wants to discuss the order he may do so AFTER he follows the command. Inform him that he is treading close to insubordination and that he needs to follow orders with out questions. I had a guy in my platoon who asked why for almost any command. One time he was standing up in the Jeep next to an M1 Abrams tank when the turret started turning. My Sgt. Yelled for him to look out and duck. Instead of listening to him, he looked at the Sarg and yelled “Why” and was clocked in the head by the barrel. He learned that if you don’t listen without question you could die.

Point of the story that if the solder continues to question your authority, write his ass up article 15 time. If you don’t listen, it can cost lives.

Any time I was Assigned a supervisory position I always let my staff know I didn't Place my self above them in any way. It wasn't uncommon to see me in their areas of work assisting when I had time. But I also made sure that they understood I didn't have time to do all tasks by my self so it was my job to assign tasks to those that was best suited to handle the task at hand. It all comes down to supervisory style. The one that leads by example (will get in there and show they aren't above getting dirty to accomplish the mission), the one that leads by directing(through mutual respect and effort), and the one that leads by force of Rank (do it or else). All are effective but not for every one and not for every situation You just have to figure out which works best for you in your situation.

Uh, speaking as an amateur historian there is nothing new about these problems. In fact in terms of things like respect of ranks and uniformity is very high compared to history. Camaradery, however, is at an all time low.