It’s just part of my routine: I do it after my usual 10-minute workout in the morning, so it has never felt like a burden.

Another, more natural way to say this is: "...it has never felt like a chore."

If I feel like/that I’ve overeaten, the scale reflects that the next day or the day after.

But I believe this routine works well for me: weighing myself daily minimizes changes and helps me put the brakes on before I gain weight.

Great use of the expression "put the brakes on"!

Thanks to this habit, both my weight and body fat have stayed stable over the past year or two.

"stayed stable" is correct, but here are some other options for your consideration

1. "remained stable"

2. "remained consistent"

The fluctuation is usually no more than about onea kilogram.

I feel like—given that your native text is written in the plain form—you could adjust this to be:

"The fluctuation is usually no more than about a kilogram or so."

or

"—and when it does fluctuate, it is usually by no more than a kilogram or so."

("Thanks to this habit, both my body fat and weight have remained stable over the past year or two—and when it does fluctuate, it is usually by no more than a kilogram or so.")
*For this sentence: I placed weight after body fat to connect it with the rest of the sentence. Since I am not sure if body fat is measured using kgs or percentages (like it is in the west): I emphasized the topic of weight as it is more strongly associated with kg measurements (if I am wrong, the sentence can be adjusted as needed—but this hopefully at least provides a good framework)

"a" sounds more natural for a single thing than "one" in most cases—and "or so" is another useful tool to emphasize the imprecise nature of a numeric value that is usually limited to—but tremendously useful—in neutral/less-formal writing.

If I feel I’ve overeaten, the scale will typically reflects that the next day or the day afteron the following day(s).

My body is very honest (with me) like that.

I feel like this flows a bit better, and adding (like that) at the end helps to connect the thought to the previous sentences.

One of my friends, after finding out that I weigh myself daily, teased me by asking, “Aren’t you a bit obsessed?” That, which made me wonder if I was overthinking itperhaps I had been over-fixating on this.

You probably won't find "over-fixate" in a dictionary, but I feel like it probably captures the nuance of 気にしすぎる a bit better than "overthink" in this particular context

Another example that doesn't involve stretching the language this much would be "...which made me wonder if perhaps I had become too (fixated on/worried about) all of this"

But I believe (that) this routine works well for me: weighing myself daily minimizes changes and helps me put the brakes on before I gain weight.

Nice use of the colon by the way -> ":"

It's a pretty cool symbol, in my opinion.

It’s just part of my routine:. I do it after my usual 10-minute workout in the morning, so it has never felt like a burden.

Someone else can correct me, but usually we don't put ":" to break up a sentence. The only time I ever use it is if I am going to list something with breaks. Like if I was going to highlight an example.

An example would be like:
- example 1
- example 2.

TheI fluctuation ise usually no more than about one kilogram.

"The fluctuation" sounds like it a process that is separate from yourself.

What you have is great. If I was going to write the sentence I would do it like this though:
I fluctuate usually around one kilogram.

But I believe this routine works well for me: weighing myself daily minimizes changes and helps me put the brakes on before Inot gain weight.

"put the brakes on" is a coloquial phrase usually you include the thing you are putting a breaks on.

For example: Raising taxes now would put the brakes on economic recovery.