Black Widow's web is a word-association map that needs to be filled out. Each word or phrase in the web is connected to other words or phrases that are associated to it in some way. Blue hubs are categories – every green word connected to a blue hub is a member of that category. Here's the full web:

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The flavortext suggests that Black Widow has caught many disguised flies in her web. There are 9 entries in the web where replacing a word with "fly" results in a common word or phrase. The 9 replaced words can be entered in the blanks at the bottom of the puzzle in alphabetical order. A good way to notice this pattern is to realize that the only word in the web that fits in the last set of blanks is "Writing's".

One of the blanks in each word has a number underneath it. Putting the numbered letters in order spells the answer, BLACK BELT.