Single word for the quality of being waterproof — "waterproofness", "waterproofity", something else?
Solution 1:
Waterproofness as a noun does indeed exist.
Solution 2:
Despite a comment to the contrary, impermeable has a sense meaning waterproof: “not allowing passage, especially of liquids; waterproof”. Also consider hydrophobic, in its sense “lacking an affinity for water; unable to absorb, or be wetted by water”; and at a bit more of a stretch, insoluble.
For a noun sort of word, besides previously-mentioned waterproofness consider hermeticity, "the condition of being hermetic (airtight)". While hermetic refers to air-tightness or gas-tightness, it is sometimes used to describe diving chambers, which are both air-tight and water-tight, and also is used to describe underwater assemblies. For a watch, either of hermetically sealed or water-tight might do.
Solution 3:
As others have said, waterproofness does exist. The OED lists a 1943 citation:
They offer advantages over certain other cellulose thermo-plastic adhesives by reason of their great toughness, waterproofness and heat sealing properties.
along with another quote from the late 1970s that also references research from that same era:
The old style boot greases were developed during World War II for government use. Waterproofness of combat boots was the main objective.
Interestingly enough, even though the OED had an entry for waterproofness, there was no entry for soundproofness, fireproofness, or bulletproofness. That means, I suppose, I can talk about the waterproofness of my watch, but I'll need to find some other way to describe the the fireproofness of my pajamas, the soundproofness of my recording studio, and the bulletproofness of my limosine's windows. Weatherproofness, on the other hand, is listed as a word.