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The mind is still part of the brain

For normal operation the brain requires certain levels of blood glucose. In order to support these telekinetic powers the brain must kick into overdrive consuming vast amounts of blood glucose.

Low levels of blood sugar can cause fainting, coma, confusion etc (look up diabetes).

What's cool about this is the body can grow to produce higher levels of blood sugar (based on constant demand) such that it represents a growth curve for your power as well as moveable maximums and plenty of possible side effects.

For instance if he becomes very powerful, he would have to use his power just to maintain healthy levels. Drugs could also influence his power.

The inverse square law, which means that, just like gravity sound and light, the strength of your TK rapidly weakens the farther away your target is.

https://en.wikipedia.org/wiki/Inverse-square_law

The inverse-square law, in physics, is any physical law stating that a specified physical quantity or intensity is inversely proportional to the square of the distance from the source of that physical quantity. The fundamental cause for this can be understood as geometric dilution corresponding to point-source radiation into three-dimensional space (see diagram).

Notice how at 30 meters, the TK power isn't 1/3 of the 10 meter power, it's 1/9.

Distance Power
 2.5m 1600%
 5m 400%
 10m 100%
 20m 25%
 30m 11.11%
 40m 6.25%
 50m 4%

Why not go the Lovecraftian route with the powers having an insanity inducing effect or other terrible cost?

In Lovecraftian fiction magic often had a great cost involved with it. There were some spells that required certain requirements to be met, but there were also spells that could be done as often as possible. Of course if you did too many of those you would go insane or attract the attention of some cosmic horror.

Perhaps there is no limit to the telekinesis in theory, but in practice there is something that makes it ill-advised to do so. Perhaps if the vigilante overexterts themselve his/her mind will start attacking itself for example; shadow enemies pop up that can destroy somebody mentally, seeing things that aren't there.

Alternatively, maybe the use of powers attracts some extremely tough enemy. There's nothing preventing the vigilante from using their powers a lot, but...it attracts some bad things. Sort of sucks saving the city by using a lot of your power if you are going to get hunted down by some insanely powerful enemies the next day depending on how close said enemies are.

Would Allomancy have been so good to use if Steel inquisitors could sense and pinpoint every use of it from across the Final empire?

Newton's second law

Much like Coinshots and Lurkers, have an equivalent but opposite force on the body of the vigilante. So he'll be limited to only light objects if he wants to stay in place himself. Or use it to throw yourself around, like Vin with her horseshoe technique. (For those not recognizing the names and terms, they're all from mistborn which the Question asker mentioned.)

Get creative. What happens if I push all air around me down ? Will I go up ?

Get Tired

Using the power tires you slowly. Compare it to mistborn's pewter drag - once you stop you drop down really, really tired.

How to limit your range

Have getting tired(or any other disadvantage) increase with the range. In general, linear composition will make it fairly easy to do stuff at range, polynomial limits you a bit more and exponential limits your range even more severe, but gives you slightly larger leeway at the start compared to polynomial. For reference, see this picture from wikipedia:

The red line is linear, the blue line a polynomial, and the green one is exponential. Your distance would be the X-axis and your getting tired/other disadvantage the Y-axis.

Torque could also be a limiting factor. The torque required for lifting, or sideways pushing, a 1kg object at 1m could only move a 100g object at 10m, or a 10g object at 100m.

Pushing or pulling an object straight away or towards the telekinetic doesn’t involve any torque, so if that was limited by the inverse square law, then doing actions which additionally required a torque would become significantly harder the further away it was. It might be easier to just get up and turn the dial on the TV than doing it with your mind, but pushing the off button might be easy.

The Mind is a Muscle

The mind acts as any muscle, it becomes tired. With practice, the mind can grow in power...as well as physically. The mind is located in the brain, and with the practice of telekinesis, it starts to expand and push against the brain. Symptoms of an oversized mind would most likely include symptoms of chiari malformation. Severe headaches, poor fine motor skills, dizziness, difficulty swallowing, vision problems, and problems with the heart and breath should provide enough motivation to stop using telekinesis for a while, however, your choice of where the mind is located will change the problems caused by overuse of the mind.

If you want to avoid these problems, as well as the problem of the lack of blood to the brain that Anon mentioned, you could stick the "mind" in the heart. Its growth would cause cardiac issues and could (maybe) make the person with an overused mind become out of breath and be forced to go to anaerobic respiration because of exercise quicker than they would if they had a weaker mind.

Pain and fatigue

This plot element was used perfectly in Stephen King's book Firestarter, where Andy McGee could use the push, which was a hypnotic suggestion that could not be resisted. However, each time he used it, he experienced a splitting pain that took a while to go away. The more he used it, the worse this pain would get until, theoretically, it could even kill him. You don't have to use this exact side-effect, but you can safely base it on this, where use of this superpower causes physical pain over time. Just like someone can throw their back, your magical friend might throw his mind!

Some examples of the cost of using powers:

1. Wheel of Time - All men who use magic are corrupted by the magic itself. If they use too much magic, they will eventually go mad.




2. Darker than Black - An anime with power-users called contractors. Every time they use their powers, they need to pay a price. The price is different for different people. The protagonist needs to smoke a cigarette after using his power but some other person has to dislocate one his fingers every time. I don't remember if the cost had any relation to their powers.




3. Sanderson's other books - See what cost he uses in other magic systems.

Just like in Eragon, magic is not "magic"... You can "force push" a 100kg block, but this will require the same energy that you need to physically move it with your muscles. Maybe the recovery time for this can be longer, so you can actually move something very heavy but you'll need to rest for very long before being able to move again.

For this reason you are forced to think carefully. Moving a 1-ton block away from you is feasible, but it is much easier to flip the switch on the crane and let the machine do the work for you...