@BlackKitKat_0707 There aren't many laptops that are lightweight, can handle Sims 4 on ultra graphics settings, have a decent battery life, and don't look like gaming laptops. It's just a very difficult thing to accomplish: even entry-level gaming hardware draws a lot of power, bigger batteries weigh more, and so does the cooling apparatus needed to keep that powerful hardware from overheating. Still, you do have some options, depending on what your priorities are.
The only laptop that fulfills all your criteria and is anywhere your price range is the Asus Zephyrus G14. It's light and a bit smaller than most gaming laptops, it has a very good battery life for what it is, and it could pass for a medium-strength office laptop if you didn't look that hard. Its basic configuration is $1,100 at Best Buy, although you might find it a bit cheaper from third-party sellers on the Amazon or Walmart sites.
https://www.bestbuy.com/site/asus-rog-zephyrus-g14-14-laptop-amd-ryzen-7-8gb-memory-nvidia-geforce-gtx-1650-512gb-ssd-eclipse-gray/6403425.p?skuId=6403425
The cheapest Dell Inspiron with a gaming graphics card is also a good choice. It's not as highly rated as the Asus but is certainly fine, it has a decent battery, it's lightweight, and it's currently $1,000 on the Dell site:
https://www.dell.com/en-us/shop/dell-laptops/new-inspiron-15-7000-touch-laptop/spd/inspiron-15-7501-laptop/nn7501eiivh
If you like Dell laptops, this one is also worth considering. While its processor is weaker than the Inspiron's, it's still more than good enough for Sims 4, and its graphics card is maybe 40-50% faster for gaming. This model comes with 16 GB RAM as well, which is nice to have if not strictly necessary. It's significantly heavier though.
https://www.dell.com/en-us/shop/gaming-laptops/dell-g3-15-gaming-laptop/spd/g-series-15-3500-laptop/gn3500eineh
The Lenovo Ideapad gaming laptops are good options in general, but maybe not for you: they're around 5 lbs, and their battery life isn't great. For the Thinkpads with only integrated graphics chips, those chips aren't fast enough to handle much more than medium settings, at least not if you're installing most of the expansion packs. This Lenovo Yoga does have a faster chip though, one probably capable of medium-high graphics:
https://www.lenovo.com/us/en/laptops/yoga/yoga-2-in-1-series/Yoga-7-14ITL5/p/82BH000AUS
The specs page doesn't list the battery for this particular model, only the upper limit for the line. So if you're interested in this one and want me to figure out what battery this exact model has, let me know.
The batteries in Inspirons with the same processor and graphics chip have enough capacity that they should provide good if not outstanding battery life; Dell also does a good job overall keeping power use down compared to similar laptops from other manufacturers.
https://www.dell.com/en-us/shop/dell-laptops/new-inspiron-14-5000-laptop/spd/inspiron-14-5402-laptop/nn5402ejobh
https://www.dell.com/en-us/shop/dell-laptops/new-inspiron-15-5000-laptop/spd/inspiron-15-5502-laptop/nn5502ejrih
Beyond those options, you'd be making a compromise somewhere. For example, these HP laptops can be customized to have an Nvidia MX450, maybe 25% faster than the MX350 in gaming. You could do so and increase the storage to 512 GB while still staying significantly under budget. However, these models' battery life is fine overall but not great for their class of laptop.
https://store.hp.com/us/en/pdp/hp-pavilion-laptop-14t-dv000-touch-optional-1s961av-1
https://store.hp.com/us/en/pdp/hp-laptop-15t-dw300-touch-optional-1b9n3av-1
This Asus Zenbook is lightweight, has a good battery, and comes with an MX350, but it only has 256 GB storage. That should be enough for all your Sims 4 content and regular schoolwork, but you might run short on space if you have large projects that take up a lot of space.
https://www.bestbuy.com/site/asus-zenbook-14-laptop-amd-ryzen-5-8gb-memory-nvidia-geforce-mx350-256gb-ssd-light-gray/6403819.p?skuId=6403819
This Vivobook has an MX350 and 512 GB storage, but only an okay battery:
https://www.newegg.com/black-asus-vivobook-k513eq-ph55-mainstream/p/N82E16834235587?Item=N82E16834235587
I know these are a lot of options to process, but the point is, you can get most of what you want. The question is where you're willing to compromise, or whether you'd rather pay more so you don't have to. If you have more questions, please feel free to ask.