I understand where you're going with this (and your frustration), but I could not find any correlation whatsoever between productivity and either height, weight, age, or method of acquisition.
Let's take a look and see the receivers that the Pats have added in the Belichick era. Players that never made a roster were not included.
2000:
Shockmain Davis (23) 6-0, 205 - UDFA
Curtis Jackson (23) 5-10, 190 - UDFA
Chris Calloway (32) 5-10, 188 - vet FA
2001:
Fred Coleman (26) 6-0, 190 - FA
Bert Emmanuel (31) 5-10, 180 - vet FA
Charles Johnson (29) 6-0, 200 - vet FA
David Patten (27) 5-10, 190 - vet FA
Torrance Small (31) 6-3, 209 - vet FA
2002:
Deion Branch (23) 5-9, 195 - 2nd round, 65th pick
David Givens (22) 6-0, 212 - 7th round, 253rd pick
Donald Hayes (27) 6-4, 220 - FA
2003:
Bethel Johnson (24) 5-11, 200 - 2nd round, 45th pick
J. J. Stokes (31) 6-4, 218 - veteran FA
2004:
Kevin Kasper (27) 6-1, 197 - vet FA
P.K. Sam (21) 6-3, 210 - 5th round, 164th pick
2005:
Bam Childress (23) 5-10, 185 - UDFA
Andre' Davis (26) 6-1, 195 - FA
Tim Dwight (30) 5-8, 180 - FA
2006:
Reche Caldwell (27) 6-0, 215 - FA
Doug Gabriel (26) 6-2, 215 - FA
Jabar Gaffney (26) 6-1, 205 - FA
Chad Jackson (21) 6-1, 205 - 2nd round, 36th pick
Kelvin Kight (24) 6-0, 209 - UDFA
Jonathan Smith (25) 5-10, 194 - FA
2007:
Randy Moss (30) 6-4, 215 - trade
Donte' Stallworth (27) 6-0, 197 - vet FA
Kelley Washington (28) 6-3, 218 - vet FA
Wes Welker (26) 5-9, 190 - trade
2008:
Sam Aiken (28) 6-2, 204 - FA
2009:
Julian Edelman (23) 6-0, 198 - 7th round, 232nd pick
Joey Galloway (38) 5-11, 197 - vet FA
Isaiah Stanback (25) 6-3, 216 - FA
Brandon Tate (22) 6-1, 195 - 3rd round, 83rd pick
2010:
Taylor Price (23) 6-0, 204 - 3rd round, 90th pick
2011:
Tiquan Underwood (24) 6-1, 180 - FA