how many weeks would you wait before giving up on treatment/medication?

This is something that should really be discussed with the doctor who prescribed you that medication, especially if this is part of a long-term treatment plan.
They'll know how much longer you may need to spend for those specific meds to work. If they still don't work, then let your doctor know and they'll advise you on how to taper off the meds (if there's any possibility they could cause withdrawal) and should then prescribe you an alternative medication which will hopefully be more suited to you.

i tried, he just said to 'give it more time.' but how am i supposed to trust his judgment when i feel worse now than i did in the beginning : /

If you feel your doctor isn't taking your concerns seriously, it might be worth consulting a different doctor for a second opinion or finding a new healthcare provider entirely.

Just speak frankly about how the side effects are effecting your day to day life and ask for a concrete idea of how long you should wait before you both consider alternative options.
Depending on the medication they might only wait a short period or they might wait for some time. A lot of psychiatric medication can take at least 4 weeks (or even up to 6-8 weeks sometimes depending on how your body responds to it) to begin noticing significant changes. Some also have noticeably worse side effects or can make you feel worse in the first few weeks or month or so.

ok, i'll press him for a more concrete answer next time. btw, can i ask you something, since you work in the health sector (if i remember right)? do you think it's unusual that he's now changed my appointments from monthly to every two weeks? i feel like i might've shot myself in the foot by mentioning sui thoughts again, but i'm not sure if that would be the reason. like, maybe he's just trying to make extra money or something bc it seems excessive. but idk, are 'biweekly' appointments a thing? am i just being paranoid?

I'm not a clinician and don't work in patient facing settings so I couldn't say really, although my workplace requires fortnightly updates from people so that seems routine to me...? (Obviously not for NHS care but otherwise...)
Given that you're evidently being started on a new medication I think (based on my own experiences as a patient) it probably makes sense they want to monitor you regularly during the initial take up of it to see how you respond, if there are any concerning side effects (and if they go away), etc. Even on the NHS when I started on a new medication they usually wanted to follow up with me within a month at least initially.

Depends on the severity of the side effects. As an allergic person if I have an unwanted reaction to a medicine I usually stop taking it. If it is a predicted reaction to the way the medicine works I would continue taking it and will talk to the doctor about the side effects.

In the past, I've held on for 3-4 months if the side effects weren't too bad, and a week when they were.
Re appointments every 2 weeks, my GP usually sees me every 2 weeks if I'm starting a new med or they deem me to be at risk/unwell.
Sorry you are having a bad day

it's nothing super serious. just annoying stuff like tiredness, blurry vision at times, and sleeping a lot during the day/can't sleep at night kind of situation.. and just feeling weird in general tbh

Haha, looks like my normal situation the last few months.
Maybe you should take something to get rid of these side effects. Some meds take time to kick in. Talk to your doctor about it.