What does it mean to worship someone or something?
Speculating first, before checking my dictionary for the word’s etymology, I’d suppose that to worship is to attribute worth and worthiness to what you then revere; to hold it in high esteem and, in the extreme, to idolize it.
In olden days, people in stately places were called “your worthiness” or “your worship.” Therefore, I’d say that to worship is to honor someone or something as possessing great goodness, virtue or value and possibly, but not necessarily, divinity.
Idolatry on the contrary, implies false worship, holding in high and reverent esteem what is unworthy, even baleful and pernicious, such as worshipping Satan.
To gauge people’s characters, discover what it is they worship, what they revere, esteem and devote themselves to regarding and to doing. By that shall you know them.
Now, to the dictionary.