ADTOE was still too heavy for me.
There are many ways I could describe ADTOE, but "heavy" is not one of them (with the exception of BITS)
See, I would consider OTBOA heavy. It's not their heaviest song, but it's got its share of E-string plam muting and double bass, and it's mostly a song driven by distorted guitar. It has its share of cool, progressive parts, but overall, it's on the heavier side. I think it's a good song, though.
BMUBMD I would also consider on the heavier side of DT. I like its slower tempo, though, and I do think it's a great song, but it's on the heavier side. It also uses the 7-string guitar, which gives it an extra heavy sound.
And despite starting out quiet, LNF gets heavy pretty fast. There's some parts of that song that, if you took out the vocals, you'd think it was Pantera. The jam session is pretty awesome though. Not their heaviest song, but it's still on the heavier side, I think.
Bridges in the Sky and Outcry are also pretty heavy.
I don't have a problem with their heavy stuff per se--after all, it was Lie that got me into the band. I got a 7-string Ibanez 15 years ago because of that song and Caught in a Web. But there's no non-ballad song on this album that doesn't still rely heavily on palm-muted guitar and double bass. That's common for DT ever after Falling Into Infinity. But listen to Trial of Tears, Lifting Shadows, Surrounded, SDV, LTL, and most of Scarred...you can go almost the entire song without hearing a palm-muted E-string.
Maybe it's just a matter of perspective. My second favorite band is Yes, and my favorite DT albums are I&W and Awake. This album still seems heavy to me.