What do I do to help with the "problem child" in my unit? How do I motivate him and others to do their job better?

I would sit down and talk to them, and find out what is going on. There may be issues going on outside of the military which could be affecting his performance. I have had Soldiers dramatically improve once they they realized what they want and that somebody had their back.

Show him the terrible job market on the outside, that should be motivational. Also, he might need a trip to behavioral heath to find the root of his binge eating and spending problem.

PFC Dennis Newport, I do commend you on stepping up to care for another warrior. If a soldier will not put forth the effort or at least attempt to improve.... sometimes even as NCOs ,there is a time to move away from a soldier.... not to misquote LTC Brown, but in my opinion this is that time. Always remember.... Soldier first, Mission always.
Keep up the motivation you have for other soldiers. You'll make a fine NCO when the time comes. Learn from each NCO you come in contact with to help develop your style of leadership good bad and ugly pick what develops YOU and how YOU want others to remember you as a leader.
I look forward to seeing you progress on here and seeing your name often as you pick up rank

It would be one thing if he was putting forth effort (any effort), but if he is just going through the motions cut him loose. You and your unit need him to be in a certain level of fitness, and when things go bad it is too late to get there. It doesn't sound like there are any other mitigating factors that would preclude you cutting him. You are not the one giving up on him, he has laready done that himself.

Would you want this guy beside you in a gun fight? Sounds like you have done quite a bit already. Seems like he has chosen his path. You need to focus on making sure you stay a good soldier and set a good example for all those around you. Sometimes that is the best thing to do. Also.....if your leadership has let that go on this long I would question if that kid is the only one who is wrong.

Chapter him. Not everyone can be saved.

It has to be more than talk. Instead of offering to run with him on Saturday, shows up to his room bright and early on Saturday and tell him it's time for a run. Make it fun so that he will want to do it again

Some people just cannot be helped. That is the bitter truth.

A long time ago when I was in the Army and this is going to sound selfish and un-Army like. The Chain of Command put more than one problem soldier in my room over my career hoping I would help them. After the first one wore me down I said to myself, never again would I bother unless the Soldier sincerely wanted my help.....it was me devising ways to make their life miserable. In my opinion you should do the same. Not your job to rehab people that can't make the cut. It is your job to help or assist the Army to get rid of them as fast as possible. Some people will not agree with me on that course of action but think about this for a moment. Your just prolonging the inevitable and endangering good Soldiers by attempting the stupid idea of attempting a salvage operation. Your being a nice guy is going to lower your morale to the point of you becomming unsalvageable. So give the guy a boot in the azz whenever you can. Drop a rifle bore brush in his boot in the morning before he gets up. Pour warm water around his waste at night when he is asleep and insist that it smells like he peed his bed the next morning. If he falls asleep during the duty day on his bed, tie his boot laces to the bed frame so that when he gets up he falls flat on his face. Flush all the toilets when he is in the shower. Stay away from electrifying his bed frame that is kind of dangerous if he makes his bed after getting out of the shower and he is still wet.........Well you get the idea. Let him know your tired of him and tired of pulling his weight. When he does screw up, point it out to the Chain of Command. Let your 1SG know in your opinion he is unsalvagable and it would be best to seperate him from the Army.

You are doing all you should and can. If you and your squad members are getting into trouble for another Soldiers actions that is wrong. Just continue to offer your support and do your job. You cannot save them all. It is your NCOs who need to do more. Thank you for your service.