Wollan is like the worst "PR" this game could have, given how he promoted the first one, even after release. If there was anything that actively stopped me from jumping on the hype train here, other than the actual quality of the first game, it was the fact that Wollan was leading the charge.
As for weight, the term is used because it really does feel like the character has weight. Strafing isn't as immediate as in COD4 (or Resistance 2, but the weightless style actually works in COD4), and you don't come to a full stop and with weapons on the ready immediately after a sprint. There's a grain of added motion to each movement, and it makes a big difference. I don't think it makes it better, but it's very functional and is certainly not worse. People who complain about any supposed sluggishness tend to be people who want it to be a COD4 carbon-copy, or people who have not actually played it themselves.