A good weight policeman won't tell you to buy an HDT or MDT, they'll just tell you to be compliant for you load and verify it properly. Other than the size of your tire or the brand, check the load ratings on the sidewall. This will provide the actual weight the tire will support (as SRW or dually). Then do the math for the ratings. Not all E rated tires have the same numerical load ratings so it's not automatic but the odds are very high they will work for you.
I also think weight police is putting the emphasis on the wrong party. If someone is non compliant they are a weight criminal. We should all be weight police, when you think about it, in that we should know and seek that we are compliant. That's my not so new story and I'm sticking to it...