Everyone has a "biggest weakness" in their game, almost by definition. Beginning and intermediate players may have many weaknesses, but there's probably a biggest. Even great players don't do everything great - it's all relative, and their biggest weakness might be something that would be a powerful strength for an intermediate player.
So what should you do about this "biggest weakness"? FIX IT!!! So how do you go about doing that?
The first step, of course, is really identifying this biggest weakness. Is it a stroking technique problem? Footwork? Weak serve or receive? Choking under pressure? Analyze your results and figure it out. Perhaps watch videos of yourself playing, and compare what you do with what top players do. A coach or top player might be able to help out in this analysis.
Once you've identified the biggest weakness, how do you fix it? To fix a stroking or footwork problem, some might do a few practice drills, or perhaps work with a coach once or twice. If it's serve or receive, perhaps they'd work on this a few times. If they choke under pressure, they'd probably tell themselves to relax under pressure and hope that solves the problem.
None of these fixes will work.
The problem with a bad habit (i.e. your "biggest weakness") is that it has gotten ingrained. You aren't going to fix it with a little practice or a few sessions with a coach. (You might quickly get it right in a drill, but under match conditions?) To fix an ingrained bad habit you have to focus on it and make it your single-minded top priority to get it right. Until you spend an extended period of time - lots and lots of practice sessions - you won't be able to undo the bad habit that you've spent your playing career ingraining the wrong way.
You also need to work with a coach or at least study videos of top players to see how the technique should be done. You don't want to replace a bad technique with another bad technique.
You not only want to turn the bad technique into good technique; you want to turn this weakness into a strength! For example, if you have an awkward backhand, don't just aim to develop a decent backhand, where if you are successful it'll be a decent backhand, while if you are "not successful" you'll continue to have a weak backhand. Instead, aim to make it a strength. If you are successful, it'll become a strength. If you are "not successful," you'll probably end up with the decent backhand you wanted anyway - and so will be successful.
To fix a bad stroking habit often you have to exaggerate the fix. For example, early in my career when I stepped around my backhand corner to attack with my forehand I wouldn't rotate around enough or bring my back foot back far enough. Because of this I could only effectively attack down the line; if I went crosscourt I had little power. To fix the problem I spent two weeks doing drills where I'd forehand hit or loop from the backhand side crosscourt with my back foot way back, and my body rotated around to the right way too much. This put me in a perfect position to attack my own forehand court (!), but not to hit to the other side. But after doing this nearly every day for two weeks, I began to naturally rotate about when I stepped around to use my forehand from the backhand side in games. After doing this exaggeration drill regularly for a few months, the problem was cured.
The same exaggeration technique works with other stroking problems. Is your stroke too long or too short? Exaggerate the other way for a while. Do you block loops off the end all the time? Have someone loop to you where you focus on closing your racket so that when you do miss, it's in the net. Can't get enough spin on your serve? Practice serving on a rug (away from the table), and focus on just spinning the heck out of ball, not caring where the ball goes, and make it jump when it hits the rug. In each of these cases, if you aren't sure about technique, see a coach or video. Be creative in finding ways to exaggerate the fix or finding other ways to get it right.
If your biggest weakness is sports psychology (such as choking under pressure), then read up on sports psychology or even meet with a sports psychologist. Then play simulated pressure matches where you start out each "match" at, say, 9-9 in the fifth. (The key is to convince yourself that these are tournament matches.)
Once you've fixed the problem, it'll be fixed for life. Then, if you dream of becoming a much better player, find the next "biggest weakness" and focus on that. Keep doing this, and you'll leave all your rivals far behind as you move up in the table tennis world.
You can spend years working halfheartedly to fix a problem in your game and never fix it. Or you can focus on the problem as your top priority for a few months and fix it, and even turn it into a strength for the rest of your playing days. Which do you choose?