You just answered your own Question:
> I've been doing it a year or two and I've gotten a lot buffer
Yes, it is possible. Its the same principle of progressive Overload for both training methods. For Calisthenics this means that after you can do a certain number of reps you switch to a more difficult Exercise. However it may take longer as you usually do more complicated movements were more muscles are involved so it is more likely that you compensate the movement with muscles that are assisting in the movement. Also some steps to the next exercise are more difficult, meaning that you may have to stick to an easier exercise because you can not perform the next one right. That is why Weight Training has usually faster results, as you can isolate the Muscles more efficiently and increase the load more easily..
>Better to use just your body than things that are completely unnatural imo
Here you make a wrong assumption. An unnatural movement would be something were you overstretch or otherwise hurt yourself. Weight Training Exercise like Bench press, Squats Dead lift and so on are perfectly natural movements just with weights attached. As your Body is literally made to perform these. If you have concerns because of the weight, that is no problem as your Body will adapt and in the beginning you are very unlikely to load up enough to hurt your Joints or Sinews.