@scotjess Are you looking to buy now? I'd be happy to help you find good laptops whenever you're ready to buy, but it's not useful to try to find the best deals now if you're going to wait. As you've seen, inventory changes quickly, and prices change even more quickly than that.
As far as the graphics card is concerned, any new-ish dedicated card other than Nvidia's MX series can run Sims 4, all packs included, on ultra graphics settings, with some room to spare. Getting a 3060 would give the laptop more room to absorb future increases in the game's demands, or perhaps a more demanding Sims 5 when it shows up, although that may well be less demanding than Sims 4 when it's first released. (That was the case for Sims 4 relative to 3.) But even a 3050 ti should always be fine for Sims 4. And I can't imagine the developers creating a Sims 5 that would require more power than that, at least in the first couple years—that would exclude a large portion of the current player base.
In terms of lightweight laptops, your options are more limited; it takes extra engineering work to fit all the components and proper cooling into a lighter chassis. For the last few years, the best option among regular (not premium-priced) laptops, in terms of price and overall quality, has been the Asus ROG Zephyrus G14. This is an example; it currently comes in at 1.7 kg:
https://www.overclockers.co.uk/asus-rog-zephyrus-g14-ga401qe-se-nvidia-rtx-3050-ti-16gb-14-qhd-120hz-ryzen-r9-5900hs-gaming-lap-lt-2ec-as.html
This is an alternate configuration that I'm mentioning because it might end up more reasonably-priced at some point:
https://www.overclockers.co.uk/asus-rog-zephyrus-g14-amd-radeon-rx-6800s-8gb-16gb-14-wuxga-144hz-amd-ryzen-r7-6800hs-gaming-laptop-lt-2h6-as.html
The G15 model is slightly heavier (1.9 kg), with a larger screen, and a 3060 instead of a 3050 ti.
https://www.overclockers.co.uk/asus-rog-zephyrus-g15-nvidia-rtx-3060-16gb-15.6-qhd-165hz-amd-ryzen-7-6800hs-gaming-laptop-lt-2h2-as.html
I don't know much about this laptop, as it's very new, but Asus does have the track record to suggest it knows what it's doing with this type of product:
https://www.overclockers.co.uk/asus-rog-flow-z13-nvidia-rtx-3050-ti-16gb-13.4-wuxga-intel-i9-12900h-gaming-laptop-lt-2hn-as.html
Other manufacturers entered the lightweight gaming laptop market more recently, so they don't have the years of good reviews to back them up, but you do have more options. For example:
https://www.overclockers.co.uk/msi-stealth-15m-nvidia-rtx-3060-16gb-15.6-fhd-144hz-intel-i7-1280p-gaming-laptop-lt-2gs-ms.html
https://www.dell.com/en-uk/shop/laptop-computers-2-in-1-pcs/inspiron-14/spd/inspiron-14-7420-laptop/cn74302sc
https://store.acer.com/en-gb/acer-swift-x-ultra-thin-laptop-sfx14-41g-blue-nx-au5ek-003
I only checked a few sites since I'm not sure whether you're looking to buy right away or are just getting a sense of the market. If and when you want help finding good sales, just ask.
And please feel free to keep asking if you have more questions in general.