To put it simply, Welker and the 2TE offense don't mix. I'm going to split everything into two categories: 0/1 TEs, and 2/3 TEs.
Tom Brady
0/1: 230/365, 63%, 2736 yds, 7.5 YPA, 23 TDs, 3 INT, 6.3 TD%, .8 INT%
2/3: 94/127, 74%, 1164 yds, 9.2 YPA, 13 TDs, 1 INT, 10.2 TD%, .8 INT%
Wes Welker:
0/1: 72 Rec, 689 Yds, 7 TDs
2/3: 14 Rec, 159 Yds, 0 TDs
Welker's stats as a percentage of Brady's:
0/1: 31% of Completions, 25% of Yards, 30% of TDs
2/3: 15% of Completions, 14% of Yards, 0% of TDs
So basically, Brady turns into Super Brady when there are 2 or 3 TEs on the field, but Welker is about half as productive. The solution? You run a 2 TE set, but replace Welker with a different receiver, one that is better in 2TE sets. I won't give the exact numbers as to avoid making this an extremely long post, but Branch jumped went from 13 to 21% in completions, and 16 to 23% in yards when going from 0/1 to 2/3 TEs. Take out his two blown coverage TDs (59 and 79 yards), and he goes from 11 to 23% in yards. Now, Branch isn't doing being productive in a 2TE offense with streaks or posts, or the short in/out option routes. He's doing it with the intermediate routes, the digs, comebacks, and curls. That's the same type of thing that Chad Johnson would do here, and I expect that he'd have awfully similar success, if not a little more.
tl;dr version:
Brady is god with 2 TEs
Welker is half as productive with 2 TEs
Branch is 1.5 to 2x as productive with 2 TEs
Chad Johnson is very similar to Branch, but quite possibly better