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I've successfully run Asset Forge on some older office PCs on medium and lower settings without much issue at all. Kenney even moved from rendered and animated previews to pre-rendered static PNG images for previews to reduce some overhead.

 Your CPU being a low powered notebook unit with weaker integrated graphics is probably the issue here. You can't swap the chip and adding an external GPU is probably an expensive and technical endeavor. Your best bet for getting more power from that computer will be adding Ram but there's no guarantee that it will help with AF as your system likely has very limited graphics capability and GPU allotted memory. I've heard of someone with a Macbook Air having performance issues too. The Air is also based on a low power Atom CPU.

Try this [Techium Eclipse] it's a Game Jam entry by Kenney that also uses Unity as the engine and assets built with some of the Asset Forge pipeline before it was Asset Forge.

I know this is probably not what you want to hear but a "new" PC may be in order. Really the requirements for Unity and Asset Forge are not that heavy so there are plenty of older PCs that can run it if you're not willing/able to build/buy a new PC for this task. Pick a processor, type it into ebay, then choose Desktop and All-in-ones and you'll find plenty of prebuilt systems. Don't get an Ultra Small Form Factor and try for a tower if possible because it will be easier to find a GPU if you need one later.