Let's take the example of red grapes used in grape juice. Grapes are healthy, right? You may have heard about anthocyamins, a class of flavinoids and resveratrol with resultant antioxidant benefits. And the rationalization continues - if I replace grapes from the vine with concentrated grape juice, I've used more grapes and that's more antioxidant value per gulp. Richly concentrated pigments in these red pigmented grapes are widely touted to be protective against cancer, aging and neurological diseases, inflammation, diabetes and bacterial infections. At this point, you are feeling pretty good about your choice and your nutrition knowledge.
So then you say, well, at least I got the benefits of the anthocyanins, etc. rather than fat and sugar alone. The health benefit of the grape juice counteracts the damage of so much sugar. Now, even if this was true, didn't you chose the grape juice for it's health benefits? At the end of this bad math and rationalization you are at best neutral for your food consumption choice. I've often seen the most educated consumers overwhelmed with the details of what they read and consequently make worse choices than if they just stayed with basic principles and logic.
If you put more than two teaspoons of sugar into your coffee or lemonade wouldn't you start to feel that it wasn't the best idea for your health? There's are very simple "solutions" to the grape juice dilemna - no pun intented. First, check the label before you purchase the juice. Water down the juice to 16 ounces and drink only 8 ounces, look for unsweetened grape juice and add your own sugar. I could tell you to buy this brand and not that one but formulas change and there is no way around looking at the food label. Just do it.
I know you really started with the best of intentions.