1. The globe-shaped portion of the eye surrounded by the socket and covered externally by the eyelids.
2. The eye itself.
tr.v. eye·balled, eye·ball·ing, eye·balls Informal
1. To look over carefully; scrutinize.
2. To measure or estimate roughly by sight: eyeballed the area of the wall that needed paint.
I think when you like to cook, sooner or later you'll become an expert in eyeballing. Sure, you read recipes, but only to find out what ingredients are needed. You don't really pay attention to the amount.
When I first dabbled in cooking, I relied on the scales a lot. And after a while, I became more relaxed and I chose cups-and-spoons method. These days, I sometimes use scales (for baking bread and cookies) but I normally just eyeball how many ingredients I'll need, how much, then go for it.
Life becomes a culinary adventure for me.
I like tweaking recipes until I find the one that suits me best. After a while, I become quite an expert of eyeballing. I rely on sense and smell whenever I cook.
I experiment a lot, too. At first, I didn't dare to do that. I might poison someone with my cooking! But now, I am more relaxed. I know the basics. I know I can mix this and that and they'll taste fab. For inspirations, I leaf my cookbooks and browse the net.
Of course, when you are a chef, you shouldn't eyeball the ingredients! You should stick to the original recipe, because you have a standard and reputation to maintain. For experiments, that's another story.
I am a mom, and I cook for my family and loved ones. So eyeballing ingredients and measurements works for me.
How about you?