Are capital letters used for terms of endearment like "Honey" and "Sweetheart"?

Both "Grammar Girl" and the Chicago Manual of Style recommend capitalizing nicknames, not capitalizing terms of endearment, and being consistent in grey areas.

GG:

"Click" and "Clack" are capitalized because they’re nicknames—they take the place of a real name. … A term of endearment isn’t interchangeable with a name the same way a nickname is, and terms of endearment aren’t capitalized.

CMS:

Chicago’s preferred style has always been to lowercase pet names, but you can’t go wrong unless you’re inconsistent, since the issue is guided by preference rather than rule.

If you are using a term of endearment as a nick-name then I think it should be capitalised (I'm Australian, hence the 's' instead of 'z'): “I love you too, Sweetheart.”

However, if it is not used as a nick-name, then it should not be capitalised: "Jack, permit me to introduce my sweetheart, Heather."

A term of endearment does not need a capital letter. However, any term that is used consistently enough to be a name should be capitalized.

A good example of how to do this can be found Fritz Leiber's short story, Kreativity for Kats, which you can read in its entirety online.

Using the name (i.e. capitalized) form of an endearment can be used to emphasize a perspective, i.e. it's a tool you can use, not merely a grammatical rule.

Uncapitalized unless it is being used as a replacement for a name. For instance, in Lady and the Tramp, Lady mistakes her humans' names as 'Jim Dear' and 'Darling', as they refer to each other by nothing else. However, even if we weren't at the dog's perspective, I'd still keep them capitalized, as they so infrequently use their real names that these endearments have effectively become their names. Lady was on to something. That's how I remember the rule, anyway.