My laptop shrinks images to fit the screen. I often edit a 3750 x 3000 original, but it isn't nearly that big when I work on it. In fact, it's about the size it'll be when posted at POTN.
Given that it is, whatever sharpening it gets ought to remain in a later viewing at that size, just as the white balance and other variables stay the same. I don't see why doing things in a different order changes the result. When you sharpen, you're just changing the colors of some pixels, right? Then, when you downsize, you lose pixels, but the surrounding ones are supposed to change again to preserve the detail in the larger version?
Your laptop only shrinks viewing size to fit the screen so you are able to see the image in its entirety. But, you are not seeing your image at 100%, you are seeing it at 25% (or whatever), so it has not in fact been downsized, or in any way altered! Open a full res file in Preview, look in the View menu (up top) and choose "Real Size" (or something similar - my Mac speaks Dutch). It will be too large to view it in its entirety; instead you will have sliders so you can scroll the image.
And so when you are viewing the full res image that your computer has obligingly shrunk so you can see the whole thing, and you sharpen that, it is not the same as sharpening a downsized version of the image. When you sharpen an image, you increase (edge) contrast, exactly the thing that is softened when you downsize it.
And by the way, you should ALWAYS sharpen your images whilst viewing them at 100%. It's the only way to determine the correct amount of sharpening.



