Volume as in bytes? It is negligible.
Overhead on checking or parsing every cell can get unwieldy if it gets big though. I have a little tool I use to parse my office printer's logs. The last one was 6,310 rows and 213 columns, and in .csv format it was 7mb, in .ods it was less than 1mb. I assume asJSON would be similar to csv.
It took around a minute to run it through my construct made parser, which goes through row by row and writes relevant information to a second array. A lua script did similarly in about 10 seconds, but to be fair I didn't really ever explore different approaches for optimizing in Construct.
As a storage medium, you probably don't have to worry about file size. Even if it somehow became an issue later, it would be simple enough to add a feature to export it into another format in chunks if so desired.