Which of the following should be used:
Swap big portions of food over smaller ones.
Swap big portions of food with smaller ones.
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That is such a great question, because the answer is nuanced.
In the particular construction that you've used, I invariably encounter "for" or "with." The question is, why?
A "swap" is an exchange of items that are in some sense of equal value, even if one is more preferable or useful than the other. In "swap with" and "swap for" constructions, there is a subtle emphasis of the equality between the items. In the construction "swap over to," the subtle emphasis shifts to the desirability of the chosen item.
Thus, "swap big portions with (or for) smaller ones" subtly implies that the choice is between to valid alternatives. "Swap big portions over to small ones" emphasizes the desirability of the preferred choice and subtly implies an inequality between the two.