Here’s a quick one, but a nice one. A dilly-house is a sandcastle—or, figuratively, a room filled with too many knickknacks.
Given that sandcastles are often typically bedecked in stones, shells, bits of seaglass and the like, it’s easy to see how that second meaning might have come along here. But how does the word dilly comes to mean “sandcastle” in the first place? That’s a trickier one.
The short answer is that we don’t know. But there are a few possible theories.
Dilly is both an old nickname for the daffodil flower, and for a light carriage or coach (originally derived from a jocular play on the “diligence” of the coach driver)—or, by extension, a wheelbarrow or similar contraption used to transport agricultural equipment or produce. Neither seems to have any connection here.
Dating from the nineteenth century at least, dilly is also an old childhood nickname for a duck. There might be a waterborne connection here, but it seems unlikely given that (with the possible exception of eider and sheldrakes) ducks aren’t readily associated with sandy beaches in the British Isles.
A more likely theory is that the dilly here is the same as in dilly-dally, a word which has been used to mean “to waste time” or “to potter” since the 1500s. Etymologically, it’s just a fanciful extension of the earlier word dally (derived from the French verb dalier, “to chat”), which has been used to mean “to amuse oneself” since the Middle English period.
This dilly carries a sense of something playful, childish, trifling, or purely for amusement. And that might make a dilly-house a house built just for fun.
Is that the answer? It’s certainly the most plausible we have on offer—but in truth, there’s still something of a question mark hanging over this one...