Based on what we have witnessed lately, the "experts" aren't.
There's certainly many health benefits to exercise, but prior to the 70s, few routinely exercised in an effort to lose weight. In fact there's a saying "You can't outrun a bad diet".
Check out photos and films from turn of the century to the 50s and 60s, most of the population was thin. Or what we would call thin today, they were of normal weight. And what today passes for normal was called fat back then. What changed in the 1970s? The misguided attempt to reduce heart disease by telling people to cut their fat intake and eat more carbohydrates (and therefore sugar, both directly and in the form of carbs that your body converts into sugar). The same photos and films will show one of the major causes of the increase in heart disease back then - smoking. We've fortunately reduced smoking rates, but unfortunately replaced it with high sugar intake, which also leads to heart disease.
One of my other interests is genealogy. I found WWI and WWII draft cards for my grandfathers, as well as some great grandfathers, uncles, etc who were the same height at me (5'8"). Interestingly enough most of them weighed 135 pounds. Both in their 30s and in their 50s. This gave me a goal weight. I'm not quite there yet, about 138 pounds now.
You cannot use current height weight tables, as they have been adjusted to reflect what the (generally overweight) population currently weighs.