what is the meaning of and they are only that in this sentence:
These intuitions, and they are only that, are based on Roemer
The words "and they are only that" form a parenthetical phrase, set off from the rest of the sentence by commas. Because it's a parenthetical phrase, it can be dropped entirely and the sentence should still make sense grammatically. Dropping a parenthetical phrase temporarily can often help you "untangle" a difficult sentence.
Dropping the parenthetical phrase gives us this:
These intuitions are based on Roemer
which is pretty simple. Now, when we put the parenthetical phrase back, it's easier to understand what it refers to:
These intuitions, and they are only that, are based on Roemer
The antecedent of both "they" and "that" is the word "intuitions," the subject of the sentence. The author is saying that the intuitions in question are only intuitions; they should not be mistaken as statements of fact, or proposals, or anything else.
This means that the author's intuitions are merely intuitions; they are not supported by experiment, research, or some other means of establishing their truth. They are to be respected as reasonable, but not trusted as authoritative.