It's even different inside the US. For example, my company currently pays all health care costs for me (in addition to the salary). But as I understand with many other (small?) companies you have to pay for the insurance yourself.
The correlation between company size and amount of insurance premium paid by the company isn't very strong in my experience, at least for tech companies. The smallest percentage I paid was at the smallest company, actually.
It's got more to do with the attitude of management, but oddly, even the companies that pay all or almost all of the premiums don't seem to discuss that.