There are 3 expiration cycles for stocks:
January, April, July, October
February, May, August, November
March, June, September, December
All optionable stocks offer options in the current month, the following month and at least the next two months in the cycle.
Of the 3,000+ optionable stocks, about 475 offer weekly options for the next 6 weeks.
A large number optionable stocks offer LEAPs (long term options expiring in more than one year) resulting in two subsequent January expirations.
Stocks and ETFs whose options are heavily traded may have even more expiration months. For example, the most heavily traded options are on the SPY which breaks all of the rules. Its expirations include:
- 16 midweek and weekly expirations
- 8 monthly expirations
- 3 end of month quarterly expirations
- 7 LEAPs expiring in various months
The short answer is that the greater the interest that traders have, the more months and the more strike prices that will be available to trade.
Here is the CBOE explanation of the option cycles.
Here is the CBOE directory of weekly options.