It's hard to get accurate numbers as many weather sites are privately held. But to give some info:
Weather Company was sold for $2B to IBM in 2015 (and recently sold to private equity for undisclosed amount). Tomorrow.IO has a $1B+ valuation pre-IPO SPAC.
That’s not really indicative of a large industry. If the weather company was bought for 2 billion, at standard valuations they were probably pulling at most 100 million per year in net income.