It's not exactly correct to call them digital amplifiers though. Class D is just a tag label, like Class A or Class A/B. The "D" doesn't stand for "Digital" it's a marketing gimmick. In the late 1990's it became a big deal to have something that was "Digital" that trend is still going on today. To audiophiles the Class D amplifier is considered part of the trendy, cheesy, home theater in a box classification.
Any well designed Class D, Class A, Class A/B, Class H, Class Whatever amplifier will be transparent and leave no mark on the sound of your system. Their are some misconceptions that Class D amplifiers can't handle complex loads, but this is not true.
The weight factor only loosely applies to like amplifier topologies. You must also not forget other weight factors, such as heat sinks, case, extra parts, or other additional weight (such as brass feet or other unnecessarily added weight).
There is nothing wrong with Class D amplifiers, they are very cost effective from just about every point of view. They are light, efficient, and are not very expensive to manufacture.