On blitz 3|2 I am rated around 1000. I love playing the game and usually I play with players around my level. I try to play against slightly better players. Assuming I am not reading chess books or otherwise get a training besides playing the game, how good should I expect to get?
And an interesting question you pose as to how good you could become playing 3|2.
The 3 min plus 2 second increment you play means roughly say a move rate overall of about say 6 seconds per move for an average game of 50 moves. You try to always play slightly stronger players, excellent idea, so assuming you are not getting trounced ie at least breaking even I think you will progress perhaps to 1200 to 1300. Games will be won or lost mostly by one or two move combinations or simple oversights by you or your opponent. Not an issue if you are playing mainly for the enjoyment of chess.
But if your real focus is to become a strong player this is a different matter. To put your question into perspective consider other endeavours. Would you expect a carpenter who only built small wooden boxes in five minutes to be able to build you a good house? A computer programmer who only spent six seconds on each line of code to become an excellent programmer without further study or deeper reflection?
If your main goal is to improve you need to start playing longer games and to play through master games that are annotated. You will notice a more rapid improvement in your games though it will require some dedicated work. Don't go overboard on opening theory, just aim to get a playable position out of the opening.
But it is in the end-game that playing strength really shows so make some serious effort in this phase of the game and you will improve dramatically. After studying endings you will find your middle game will start to improve as well because you now are aware of which endings to aim for and which to avoid.
Before the internet era I did not have much chance to play over-the-board so I played correspondence chess. This long style of chess forces you to carefully analyse your moves and to study openings and endgames otherwise you could be stuck with a bad position for a year or two! When I did get to play OTB I did regularly get behind on the clock but managed to bowl over quite a few strong players including some with titles.
Improving at chess for many people means obtaining a better understanding of different aspects of the game, such as: how to play different types of openings, different midgame plans and how to undertake them an defend against them, and how to play endgames well. Underpinning all of the strategies and knowledge is a level of competence in tactics. It is this wider understanding that stronger players draw on when playing blitz that enables them to make good moves quickly.
Playing blitz 3+2 is giving you plenty of practice in spotting tactics and ideas quickly. Unless you are spending some other time thinking about the games, you are limiting your potential to that single improvement method. And there is nothing wrong with that if you enjoy the games. However, if you want to achieve your full potential, it will almost certainly help to think about different aspects of the game for more time than you have per move at blitz. This might be by playing some games at a slow time where you can have a proper think about options, by reviewing some key positions with a friend or a computer program to understand how different choices might play out, or by some reading.
If you don't fancy the idea of any of that, there's nothing wrong with continuing to learn by doing. Choosing to play against people slightly better than yourself is sensible in that regard - on the occasions they beat you they will often use ideas that you can understand and learn from.
You asked in a comment above how to benefit from analysis of your own games. One way is just to notice the questions that you ask yourself during the game, and occasionally follow them up. For example, you may feel during a game that you have a great attack but the opponent wriggled out of it. Looking at it afterwards with a computer will either tell you how you could have closed in on checkmate, or confirm that the attack was unsound. Then you will have either some improved ideas about how to conclude an attack or a slightly improved feel for whether an attack is worth launching. Other common questions are "where did I go wrong in this game", or "how do I deal with this opening line that people keep beating me with"? But follow your own interest.
My rating was 1400 on chess.com three months ago. After that I stopped playing. But I got this rating by playing and analysing my games only. So you can get upto this level without reading or taking any training. About rating like 1700 or 1800 I don't know much about them as I never got upto that level.
Hope it helps.
I don't think there is a general answer to this that will fit everyone. A really astute individual or a savant will be better at spatial relations and interpreting the basis of the game than the general run of players. Players like Morphy or Capablanca, of whom it was said that chess was his native tongue, would fit that description. A keen observer would understand that the game is a dynamic balance that must be upset in one's favor to win. Tactics utilized to win material, basically spatial relations, may come more naturally to some than others. I taught myself to play as a youngster in 1948 but always attacked the king directly at the expense of material and didn't grasp the concept of gaining a material advantage first until I was given odds in a game with an Expert teacher. Then a light bulb went off in my head and I immediately understood that I had to win material before going after the king. Understanding of strategy took longer and relied mainly upon book learning from a manual. That's just a shortcut to avoid all the mistakes that would go into experiential learning, which for the normal person would take many, many games. I really don't think limiting yourself to quick play as you mention is going to let you understand some of the more profound aspects of the game either. Fischer said that blitz kills ideas. It's more reflex than understanding. I personally would suggest longer games for that purpose, along with some book study to shortcut your learning by trial and error. And playing stronger players is alway desirable for progress. If you're very clever, you could probably advance into the average ranks by play alone, but unless you're exceptionally gifted, going much further isn't likely to happen without some study.
As others have indicated, without extra work, you will hit a ceiling beyond which you won't move. Where the ceiling will be will depend on how smart you are. I've only been playing and watching GM games, some videos, never really seriously read any books and I've been stuck at about 2000-2100 for about a decade. But take Morphy, for example - he mostly relied on his natural ability (there was not much theory then) and experts agree that he played at a GM level.
It really is rather sad that nobody has mentioned going over the game with your opponent afterwards. Of course with so much chess being played online these days this is often difficult, but it forces you to try and explain what happened, and to invent your own theories that can be compared with what you find in books. Not everyone is able to learn from this. For some it is just a continuation of the combat. Avoid these people.