The adverb widely is good for describing something that happens over a broad area or in a big way. If it is widely believed that the stock market will crash, then you better sell, sell, sell.
If the houses in your neighborhood vary widely, there is an enormous amount of difference between each house — a tiny bungalow next door to a huge mansion, for example. Likewise, when you smile widely at a cute little kid, it's a big smile. The adverb widely comes from the adjective wide, or broad, from an Old English root word, wīd, "spacious or extensive."