How am I gaining weight

I’m gaining weight despite literally eating in a caloric deficit. I ate a lot of Easter but I’ve been eating literally 500 calories a day since then and I’m not miscounting. I eat a banana and a packet of instant noodles, the banana is 100, the noodles are 400. I ate a lot on Sunday (approx 2500 calories) but have had just a banana and noodles for the past two days and I’ve still gained a kilo. I’ve gone up from 40kg to 41kg. This shouldn’t even be possible and it’s driving me crazy. Am I just doomed to be fat? I’ve been exercising like normal as well but still gained the weight.

How tall are you and how old are you that you want to lose weight from being 6 stone?
Go and see your GP to get proper advice on nutrition and health, as eating only 500 calories of pretty much rubbish, plus exercising, will not do you any good.

I’m 5’0 and 20

I’m gaining weight despite literally eating in a caloric deficit. I ate a lot of Easter but I’ve been eating literally 500 calories a day since then and I’m not miscounting. I eat a banana and a packet of instant noodles, the banana is 100, the noodles are 400. I ate a lot on Sunday (approx 2500 calories) but have had just a banana and noodles for the past two days and I’ve still gained a kilo. I’ve gone up from 40kg to 41kg. This shouldn’t even be possible and it’s driving me crazy. Am I just doomed to be fat? I’ve been exercising like normal as well but still gained the weight.

So you're already underweight and trying to lose more weight? See your GP.

I know what a doctor would tell me but they don’t take body type and aesthetic preference into account when deciding what a “healthy weight” is

You can't measure weight gain/loss over 2 days.
500 cals a day is nowt to do with 'aesthetic preference', it's likely actively harmful. "I can't see my doctor because they will tell me to stop" is also a remarkable take.
Case in point, you are 300 cals a day below where the ASA requires any diet scheme to come with a disclaimer/health warning.
https://www.bbc.co.uk/news/entertainment-arts-68713464

You're not fat, and if anyone here were to provide you with the advice you're looking for they would be incredibly irresponsible.
Your current weight already puts you at risk of having a compromised immune system and premature death. If you lost 5kg you'd be putting yourself at risk of severe illness and hospitalisation. 10kg and your organs could start shutting down.
You don't need to lose weight. Your aesthetic isn't as important as your life. You need to see a GP - and please do so quickly.

I’m maintaining my current weight, I’m not aiming to lose a significant amount more

I’m gaining weight despite literally eating in a caloric deficit. I ate a lot of Easter but I’ve been eating literally 500 calories a day since then and I’m not miscounting. I eat a banana and a packet of instant noodles, the banana is 100, the noodles are 400. I ate a lot on Sunday (approx 2500 calories) but have had just a banana and noodles for the past two days and I’ve still gained a kilo. I’ve gone up from 40kg to 41kg. This shouldn’t even be possible and it’s driving me crazy. Am I just doomed to be fat? I’ve been exercising like normal as well but still gained the weight.

500 calories a day isn't a weight maintenance. That's restricted dieting. What you're doing is extremely unhealthy and could cost you your life. Please seek medical help before it gets to that point.

On a normal day I eat 1000-1200 calories a day, I’m just making up for the cheat day rn

Even 1200 is still dangerously low. It might be enough for a toddler, but certainly not enough for a 20 year old. Your body will start to shut down (if it isn't already) and your life will be put at risk. Please see a GP before things spiral completely out of control.

I’m 5’0 and 1200 is near enough my maintenance calories even with doing 10,000 steps a day, plus I spend a lot of time making up for cheat/binge days. There’s nothing a GP could do for me that I actually want

If you consider a lot of days as 'cheating' and 'binging' see your GP, as you have an unhealthy relationship with food. If you eat at maintenance calories, then exercise, you are putting yourself below the number of calories required to maintain your weight and will lose it.

I’m gaining weight despite literally eating in a caloric deficit. I ate a lot of Easter but I’ve been eating literally 500 calories a day since then and I’m not miscounting. I eat a banana and a packet of instant noodles, the banana is 100, the noodles are 400. I ate a lot on Sunday (approx 2500 calories) but have had just a banana and noodles for the past two days and I’ve still gained a kilo. I’ve gone up from 40kg to 41kg. This shouldn’t even be possible and it’s driving me crazy. Am I just doomed to be fat? I’ve been exercising like normal as well but still gained the weight.