Simba has it right.  The smaller the laptop and longer the battery, the more limited the CPU will be.  Not to mention it will be more expensive and harder to repair.
You can find laptops that are under 2.5 pounds and run for a whole day, but they can't handle much more than a couple of web apps without lagging, and forget having allot of programs open at once.
Unfortunately, you'll just have to make a compromise between weight and power.  However the gap is shrinking more and more lately.  These days, you can get a laptop under 3.5 pounds and less than 3 quarters of an inch thick and 12 inches wide that does everything a 15 inch 5.5 pound 1 and a quarter inch laptop could do 5 years ago, and you'll get half again as much battery life out of it too.

mainly my tasks include programming and writing

If programming means JavaScript or Python, anything is fine.  If programming means Java, C#, or something else compiled you really, really want something more powerful.  To put this in perspective, I've got the typical overpowered programmer tower with 6 cores and a super fast SSD and all that, and something like Synthizer (C++, 10000 lines or so including dependencies) takes around 30 seconds to build from scratch.  If I was doing it on an Air...well, I can't imagine doing it on an air.  This may not sound so bad, but keep in mind that programming often means that you change 5 lines and rebuild the entire thing, you really don't want the edit-compile-run cycle to be slow.

If you're only going to run Windows, Macs tend to be overpriced and you can probably get a better deal by shopping around.

While the ultra-thin laptops seem really cool, going an extra half centimeter thicker and maybe up to a 15 inch or 17 inch can get you all the way to what is basically a portable workstation that's only 5 pounds and fits in a backpack, if you want to push it that far.  Not saying you should, just that laptops have come a long way and it's still a lot more portable than you're giving it credit for.

Yeah, if you want to do iOS then a mac is mandatory.  But light and thin, 1-2CM thick is pretty light and thin.

For app dev you don't want an Air though.  You can, but things like dart likely fall on the "expensive to compile" side of the equation, and things like Swift and C/C++ definitely do.

I guess I could get a MacBook Pro

Don't get a MacBook right now.
Mostly due to the new silicon that will be added to the Mac, it'll probably be wiser to wait. You're probably not going to be able to program for Windows on it, but it'll future-proof way better than current ones.
That being said though, I still can't recommend the Mac for programming because of how awful Voiceover is in the terminal. There have been many times where I have compiled something and VoiceOver skips errors.

Whatever you do, get a computer with an SSD. Don't bother with those stupid hybrid drives or a regular HDD. Once you use an SSD, you'll never want to go back to a spinning drive.

Everything else is up to you. Get something with at least 8 GB RAM and an i5 processor. If you think you'll need more power, go for 16 or more GB RAM and an i7 CPU.

@jayde have you ever had to use it for resource intensive tasks? And if so how did it handle them?

If you are really truly serious about making mac or IOS apps, than yeah I'd go with a 15 inch Macbook Pro 2019 model, since unfortunately the only 13 inch model they have right now is quite out of date and definitely not worth the money, and the 2020 16 inch Macbook Pro is even more crazy expensive and not actually allot different. You can get an I7 or even I9 processor, but save money by going with a 256GB SSD , which should be enough for what your doing.  If you are in school, you should also be able to get education pricing through them, and going with certified refurbished can help too.
Otherwise, you can spend allot less and get better hardware and repairability for the price with a Windows laptop.
It's not an easy choice for sure.  The mac is definitely more flexible and devalues  allot slower if you want to sell it down the line, but it will get outstripped by other machines more quickly too, while a Windows computer would keep up better but might die prematurely do to lower quality hardware, and you'd have to spend extra to get even a second hand, slower Mac to code Apple apps on if you decide you want to do both later.

@camlorn in the future after I get my computer science degree I plan to take up programming as a job although based on what I’ve heard it makes programming a lot less fun but I don’t care about that right now. I think I can afford a lot. My budget is around $3000 because that’s what I have saved up so far. I remember the last time I tried to get a cheap computer and it didn’t go well which is why I saved up for it this time

$3000 gets you a *lot*.  I would have trouble spending that much on a laptop.  I could do it, but I'd have to check all the boxes and it would be beyond anything I personally need (for example, programmers don't benefit from a GPU outside specific domains).

The CS degree may or may not make programming less fun, but the salary makes up for it and I think it would be more accurate to say that getting paid for doing anything that you used to do as a hobby probably makes it at least a little less fun.  If you're the right sort and in the right situation, a CS degree can actually be quite enjoyable: CS people are on the forefront of basically everything now, up to and including really big questions like "what is thought".  Indeed in regards to that specific example, philosophers have nothing on OpenAI employees, who are probably very much "Machines can't think? Hold my beer..." these days.  On the one hand you've got "it's all math and this sucks", on the other one of the introductory proofs most people do is "here is an example of a question that cannot be answered that we'd actually like to have an answer for. No, not even by god.", and then there's "And also some infinities are bigger than others, watch this", usually in the same class.