How can I politely tell a student that I already support him several times and that is enough?

I'll assume you already have language that indicates your support. Don't give up on that.

But, ask him for two things. First, that he only asks for feedback once a week (or whatever you are comfortable with) and add a report on changes and why they were made.

Second, ask him to specify in the report things he is unsure about and to detail why he is unsure.

The goal is to get him to think more deeply about why he is doing things and to separate the simpler from the deeper things.

I think the key here is your insistence on “trying to be polite and nice” and telling the student “politely”. I can’t say for sure, but I’m guessing your desire to be polite is getting in the way of clear communication. I’ve seen this happen with people who are so afraid of upsetting others that a lot of the time when they want to communicate something it comes out all muddled because of the insistence on passing everything through a kind of “politeness encoder”. Usually the way this happens is the person who does this tends to think that the listener knows all about this encoding scheme and can decipher the message easily by applying the inverse “politeness decoder”. But this is simply not true, and the message is lost.

Be polite if you want, but first of all be clear. Have a frank talk with the student, explain the problem as you perceive it (with the politeness encoder dialed down to a minimum or turned off altogether), and brainstorm with the student some plan to get past this obstacle in his approach. Once the student understands what the problem is, he will be well-positioned to address it.

I want to convey that I encourage them to do further research and it is okay to say something I disagree with as long as they support it with proofs and evidence.

Then that is what you should say! Precisely that.

Dear X

I appreciate your desire to get things right but always relying on others may be counterproductive. I encourage you to do further research. It is okay to say something I disagree with as long as you support it with proofs and evidence.