Most of the articles I read stated that the minerals and other benefits of blackstrap molasses balance the sugar contained in it. Here's an article naming 15 health benefits of blackstrap molasses. Still, it's best to limit the amount of blackstrap molasses in your diet, and given its strong taste and dark color, there aren't that many foods you'd want to sweeten with it.
Reading more about sugar, inflammation and osteoporosis, it seems that there is a connection. In the article, The Relationship between Sugar and Inflammation, the author points out that eating too much sugar can interfere with the body's use of enzymes and minerals, which could affect bone formation/regeneration. Another article mentions sugar as one of the foods that are "bad for your bones."
I'm learning that blueberries with a little milk can be just as satisfying as a chocolate chip cookie. Fruit has its own sugar, but combined with the fiber and nutrients of the fruit, in moderation, it won't fuel the fires of inflammation. Fruit juice is another story; it's best to eat the whole fruit instead.