First, it should be noted that in the twentieth century the prefix meta- acquired a relatively specific function, which it did not have before, and which is only loosely related to its original meaning in Greek language. This question is about this, relatively new, use of the prefix (in, for example, metadata and metatheory); the consideration of older words containing it, such as metaphysics or metaphrase is therefore not likely to be relevant.
Second, whenever an opposite of something is sought, the question arises: what kind of an opposite? Is the opposite of metaX that is sought here supposed to be (1) something that stands to X in the relationship that is the opposite of the relationship expressed by meta-, or (2) X that is not metaX? The next to last sentence of the question (about lowering as opposed to raising) seems to imply (1), but the last sentence (about cancelling out the meta-) seems to imply (2).
Now, metaX, in the sense of meta- that is relevant here, is X that is about other X: for example metadata are the data about other data, a metatheory is a theory about other theories. (Incidentally, it is misleading to say that metaX is 'about itself'; it is normally about other X.) The relationship of being about something does not have an opposite, in the way in which lowering is the opposite of raising. Therefore, if the question is seeking (1), the answer is that there is no such thing.
Let's suppose then that the question is seeking (2). In most cases, there is no need for a special term for (2); generally, X that is not metaX is referred to simply as X. MetaX is something that needs to be marked by a special term; when that special term is not used, but only the plain X, it can be presumed that ordinary (non-meta) X is referred to (or, alternatively that the distinction between metaX and ordinary X is not relevant). For example, when we hear the term data, we usually don't think of metadata, because we know that if they had been referred to, the more specific term metadata would have been used.
Nevertheless, there are some rare context in which we need to make it clear that the X we are talking about is not metaX. Thus if we have just been discussing metaX at some length, and we are now switching to discussing X that is not metaX, we need to make it clear that this is what we are doing; can that be accomplished without using the cumbersome phrase 'X that is not metaX'?
For some values of X, there may be a special term that means precisely X that is not metaX. There is thus an established term object language, which is used in contrast to metalanguage: the idea behind that term is that the object language is about extralinguistic objects, unlike metalanguage, which is about object language.
Given that metaX can be characterised as second-order X, one term than can often be used for X that is not metaX is first-order X; that term is the closest to the opposite of metaX. The only possible obstacle to using the term for that purpose in a particular context is that first-order is already used for some other purpose in the same context.