That bronze level plan costs more than twice what I am currently paying.
How old are you? If you're young that may explain what you're seeing.
Here's the deal. The individual insurance market has premiums that are heavily biased towards expected claims for sicker people, but if you look at how premiums vary by age and other underwriting characteristics, it's more proportional to how the average claims change with those characteristics.
For group insurance, there isn't as much bias towards the cost of sicker people. The contract bundles the healthy and the sick people together so healthy people opting out is less of an issue. But the demographic component of the cost is basically averaged across the group, plus there is rating based on the actual experience of the group.
The exchanges are basically a group insurance scheme. However, they do allow charging different premiums based on age. The ratio between the highest premium and the lowest premium is capped at 3 to 1, whereas before in the individual market, this was more like 6 to 1.
Monetarily, the law is going to be worst for people who are young, have good underwriting characteristics and who already have individual insurance. But you are also getting a guarantee that you will be able to buy insurance next year. You don't have that under your current plan. Also, that 3 to 1 cap will work in your favor over time. You are getting less per dollar for the upcoming year of coverage, but you are getting guarantees that extend far beyond that year of coverage.
If it were possible to buy an individual insurance policy with guaranteed renewal for life under the pre-ACA regime, I'm guessing it would have cost an awful lot more than that bronze plan since they would have to price in the possibility of you moving into a higher risk class later.