Body and gravity are related, but not exactly the same thing. In wine-making sometimes body is called "structure." In the case of wine, most of the body is coming from the yeast. There are some reds that finish very low that are almost "chewy" because they have so much body.
In beer brewing, a lot of people simply rely on their residual sugars to get the body they want. Most people focus on the FG, but it should really be the difference between apparent attenuation and possible attenuation, determined by a forced fermentation test.
A high FG with a beer that has fully attenuated means that the beer has a high dextrin content, but Charlie Bamforth studied dextrins in beer, and all other things being equal, it takes a ton of dextrins to affect body and mouthfeel. Way more than you could get from barley malt alone, you'd have to actually add dextrin to your finished beer.
A lot of Belgian strains (especially Saison strains) are thought to be descended from red wine yeasts, which is why they like higher temps, and create nice structure and body even at very low FGs. Back to the attenuation issue, I've brewed a Belgian Pale and a Saison, both had the same OG, the FG on the pale was 1.010, and the FG on the saison was 1.004, and the Saison tasted much sweeter than the pale, because the pale was closer to its possible attenuation than the saison, which could have gone lower if I had wanted it to.
You can help your yeast create structure by making sure it's healthy, pitching at the correct rate, aerating well, and controlling fermentation temps.
There are lots of ways to get more body and mouthfeel, but IMHO syrupy beer is a flaw in most styles, and are usually an indicator of not giving the yeast the time and tools to do their job. (Not that I'm accusing Spaten of that)