Anathema's death-doom era "proper" didn't last that long...it was basically their debut EP (Crestfallen), plus their first full-length Serenades and subsequent EP Pentecost III. Basically the albums fronted by their first singer, Darren White.
The first album with Vincent Cavanagh as a vocalist (The Silent Enigma) was already somewhere in between what they were and what they'd become.
My favorite phase is the Eternity- Alternative 4 - Judgement run (A4 is my #1 album from them). Absolutely fantastic stuff...a bit bleak overall (compared to the more uplifting approach of the more recent albums), but very "powerful". If one is used to Vincent's vocals now, listening to Eternity might be a bit jarring (he was still coming into his own as a vocalist there), but already starting with Alternative 4, he had matured significantly (I'd recommend at least Fragile Dreams and Lost Control). And then, on Judgement, his vocals are pretty great (Deep, the opener, is one of my favorite Anathema songs, period).
But, yes, of the phase that started with We're Here...(I think of that as their "positive-prog" phase), Weather System is my favorite (and, really, up there in their discography as a whole). It's a great, great album. And the Untouchable songs are near-masterpieces.