I would think the larger nations would be more likely to have a negative trade balance.
Not at all.
Qing China ran a huge trade surplus. That's why the European powers wanted to force them to buy opium. The Qing Empire was exporting so many goods and acquiring so much bullion that it was bankrupting many European trading companies. By the 1860's the Qing Empire's trade balance
might have been in a deficit. The Qing tightly restricted imports and subsidized exports, creating a positive balance of trade. Ultimately, however, what depleted the Qing Empire's silver reserves was not a trade imbalance (though opium expenditures did lead to a diminishing trade balance) but rather reparations payments and other treaty obligations which Western powers required them to pay.