Smaller aircraft have performed the role in the past, but the smallest current helicopter that can perform quality is a bit debatable. Depending on the dimension you're measuring, it's either the Westland Lynx/Wilcat or the Eurocopter Dauphin/Panther (and it's Chinese clone). The only other ASW helicopter in that class is really the Kaman Seasprite, though it's getting a bit long in the tooth.
So, that pretty much closes the book on the matter, doesn't it? Well, not exactly. You are correct that the NH90, Merlin, and the aircraft they replaced, the Sea King are all much bigger, much heavier helicopters. They are also much more capable. The most popular ASW helicopter in the world, however, is the SH-60/MH-60R. I would normally support its inclusion in the "mid-size" market right up there with the NFH, but it actually folds up quite nice into a really small package. It still weighs as much as the other "mid-size" helos, but it does have a lower physical footprint. That's why you occasionally see it competing in the same market space as the AW159 Wildcat where the NH90 could not (to say nothing of the Merlin!). It offers "mid-size" ASW helicopter performance for the size of a "compact" helicopter. You just might need to reinforce the hangar deck a bit and give yourself a bit more room in parts of the hangar.
The US and Australia replaced their Seasprites with the MH-60R and the Danes just replaced their Lynxes with the MH-60R. The US saw this market space shrinking and left the Seasprite without a direct "light helicopter" replacement. I think the Wildcat, much as I LOVE it, never should have been developed either (and for the same reason). The ASW capabilities of the Panther aren't nearly as robust, so it's competing in a slightly different market space. More importantly, it's just a modification of a successful civilian helicopter, not a dedicated military airframe like the Lynx and Seasprite. It doesn't need to stand on its naval helicopter merits alone to survive.
I really do think the days of the dedicated light ASW helicopter are gone, likely to be replaced by unmanned options or larger, more capable helicopters like the Seahawk and NH90. So, that closes the book on the matter, doesn't it? Well, not really. In length and width, the Russian Kamov Ka-27 offers a robust, alternative ASW capability comparable or superior to that of the "light" helicopters. It's just the ridiculous height that holds it back. You either design your ship to take Kamovs...or you don't. That's what the Russians ran into with the Mistrals.
Remember, as with everything in life, there's no such thing as a free lunch. There's always a cost, always a tradeoff.
Cheers,
Logan