What are the possible meanings of positive "any more"?

Basically, the positive anymore does not simply have the meaning of nowadays, but rather means simply quite the opposite of negative anymore. The negative anymore implies that what is described by the sentence used to be the case, and asserts that it no longer is, the positive anymore implies or asserts that what is described used to NOT be the case, and asserts that it is now.

Kindle and Sag (1975) provide a slightly more technical explanation. Consider the following:

(1) Anymore, we eat a lot of fish.

According to Kindle and Sag (1975):

The usual hypothesis advanced about the grammars of those, primarily Mid-west, speakers who say sentences like [(1)] is that they have restructured anymore into a free-wheeling lexical item with the meaning of 'nowadays'. [...] This explanation has recently been shown to be unsatisfactory by Labov (1972), who observes that all English speakers balk at items like [(3)] and [(4)].

^{(Kindle and Sag 1975:89)}

(3) When would like to live, 1920 or anymore?

(4) When was the best beer brewed? ... Anymore.

Kindle and Sag continue, quoting Labov (1972):

'In Standard English a sentence of the form: 'I don't do Y anymore' presupposes that 'X used to do Y'. In these 'positive' anymore dialects a complex semantic change has taken place creating a new lexical item anymore-2, which occurs only in positive sentences. Positive sentences of the form: 'X does Y anymore' assert that 'X didn't used to do Y.' Positive anymore speakers still have the old anymore in negative sentences, i.e. as a polarity alternant of still.'

^{(Labov 1972, cited by Kindle and Sag 1975:89-90)}

^References

^{Kindle, D. and I. Sag. (1975). Some more on anymore. In R. W. Fasold and R. W. Shuy (eds.), Analyzing variation in language: Papers from the Second Colloquium on New Ways of Analyzing Variation. Washington, D.C. Georgetown University Press, 89-111.}

^{Labov, W. (1972). Where do grammars stop? In R. Shuy (ed.), *Georgetown University Round Table on Languages and Linguistics 1972. Washington, D.C. Georgetown University Press.}

Positive anymore is a feature of the Midland American English dialect. It is the region highlighted in purple on the map below:

It has essentially two closely related meanings: "nowadays" and "presently". My parents, being from the Midlands, use positive anymore in this way.

Think of it like this: for any negative sentence in which you could use the word anymore, think of the logical opposite of that sentence — you can use positive anymore in that situation, e.g.:

• I don't wake up early anymore. -> I wake up early anymore.
• I won't help her anymore. -> I will help her anymore.

In all forms of Standard English, the word "nowadays" (or "these days", etc.) would be substituted in place of anymore, but you can probably understand the logic.

(One is also able to position positive anymore more freely than negative anymore, like at the beginning of the sentence: "Anymore, I just listen to the radio".)

Yes I have heard any more used positively in the American Southwest - meaning, as noted above, "these days." It is a regionalism, but I don't know its geographic distribution.