Why do we use 'take', and what does it mean in 'does he take sugar'?

The verb 'take' is used in the context of personal habits such as Do you take sugar?; What size shoes do you take?, Do you take the Guardian/New York Times?, even At what time do you take dinner?, or I need to take a bath/nap/look at something.

Why, exactly are we using 'take', in these instances?

I think it has to do with the semantic evolution that this term has experienced from Old English.

• OED calls take "one of the elemental words of the language;" take up alone has 55 varieties of meaning in that dictionary's 2nd print edition. Basic sense is "to lay hold of," which evolved to "accept, receive" (as in take my advice) c. 1200; "absorb" (take a punch) c. 1200; "choose, select" (take the high road) late 13c.; "to make, obtain" (take a shower) late 14c.; "to become affected by" (take sick) c. 1300.

Etymonline

I believe it's "take"; as in the sense of "accept" and "receive".

Consider a hypothetical scenario in which you are presented with some arbitrary item. For instance, a mail courier delivers you a suspicious package. You can either "accept" & "receive" the suspicious package or you can opt to "reject" & "refuse" it.
That is to say: You can either "take" it or you can "leave" it.

Of course, it doesn't necessarily have to be a mail courier and a suspicious package. It could be a friend with a gift for your birthday.. It could be a perfect stranger, offering his personal opinion.. It could be a shoe salesman enquiring about your size, or an acquaintance offering you some sugar for your coffee.

This usage always implies a choice. It's saying: 'When given the usual range of options, which do you habitually take?' In the relevant situations (serving tea, buying shoes, selecting a newspaper) the options are commonly understood, and taken(!) as read.

See also take your pick - "to choose what you want."