Does Weatherby recommend specific ammunition for each caliber to get the best accuracy?

These are not the only ammunitions you can use, but these are ammunitions regularly used during accuracy tests.

223 Remington Winchester 55gr Ballistic Silver Tip
(SBST223B)
  Federal 55gr Nosler Ballistic-Tip
(P223F)
  Barnes VOR-TX 55gr TSXFB
(21520)
22-250 Remington Barnes VOR-TX 50gr TSX
(22008)
  Winchester 55gr Ballistic Silver Tip
(SBST22250B)
  Federal Premium 60gr Nosler Partition
(P22250G)
243 Winchester Barnes VOR-TX 80gr TTSX
(21522)
  Winchester 95gr Ballistic Silver Tip
(SBST243A)
  Federal Premium 100gr Sierra Game King BT-SP
(P243C)
240 Weatherby Magnum Weatherby 85gr TTSX
(B24085TTSX)
  Weatherby 100gr Nosler Partition
(N240100PT)
  Weatherby 100gr Spitzer
(G240100SR)
257 Weatherby Magnum Weatherby 100gr Barnes TTSX
(B257100TTSX)
  Weatherby 80gr Barnes TTSX
(B25780TTSX)
  Weatherby 110gr Nosler Accubond
(N257110ACB)
  Weatherby 115gr Nosler Ballistic-Tip
(N257115BST)
  Weatherby 100gr Interlock
(H257100IL)
25-06 Remington Barnes VOR-TX 100gr TTSX
(21557)
  Federal 110gr Nosler Accubond
(P2506A1)
  Winchester 115gr Ballistic Silver Tip
(SBST2506)
6.5 Creedmoor Hornady 143gr Precision Hunter ELD-X
(81499)
  Barnes VOR-TX 120gr TTSX
(30815)
  Hornady 129gr SST
(81496)
  Federal Premium 110gr Nosler Partition
(P65CRDA1)
  Winchester 140gr Ballistic Silver Tip
(SBST65CM)
6.5 Weatherby RPM Weatherby 127gr Barnes LRX
(B65RPM127LRX)
  Weatherby 140gr Accubond
(N65RPM140ACB)
  Weatherby 140gr Interlock
(H65RPM140IL)
6.5-300 Weatherby Magnum Weatherby 127gr Barnes LRX
(B653127LRX)
  Weatherby 140gr A-Frame
(F653140AF)
  Weatherby 130gr Scirocco
(F653130SCO)
270 Winchester Barnes VOR-TX 130gr TTSX
(21524)
  Hornady 145gr Precision Hunter ELD-X
(80536)
  Federal 130gr Sierra GameKing Boat-Tail Hollow Point
(P270D)
  Winchester 150gr Nosler Accubond Long Range
(S270LR)
270 Weatherby Magnum Weatherby 130gr Barnes TTSX
(B270130TTSX)
  Weatherby 140gr Ballistic Tip
( N270140BST)
  Weatherby 130gr Hornady Spire Point
(H270130SP)
7mm-08 Remington Barnes Vortex 120gr TTSX
(21561)
  Hornady 150gr Precision Hunter ELD-X
(85578)
  Federal 140gr Nosler Ballistic Tip
(P708B)
7mm Remington Magnum Barnes Vortex 140 gr TTSX
(21526)
  Winchester 168gr Nosler Accubond Long Range
(S7LR)
  Federal Premium 150gr Trophy Copper
(P7RTC3)
  Hornady 162gr Precision Hunter ELD-X
(80636)
7mm Weatherby Magnum Weatherby 140gr Barnes TTSX
(B7MM140TTSX)
  Weatherby 120gr Barnes TTSX
(B7MM120TTSX)
  Weatherby 154gr Hornady Spire Point
(H7MM154SP)
308 Winchester Barnes Vortex 168 gr TTSX
(21541)
  Hornady 178gr Precision Hunter ELD-X
(80994)
  Federal 165gr Sierra GameKing Ballistic-Tip
(P308C)
 

Winchester 150gr Ballistic Silver Tip
(SBST308)

308 Winchester Heavy Barrel Varmint & Tactical Rifles Federal 168gr Sierra MatchKing Boat-Tail Hollow Point
(80963)
30-06 Springfield Hornady 178gr Precision Hunter ELD-X
(81147)
  Barnes Vortex 180gr TTSX
(21533)
  Federal 165gr Sierra GameKing Boat-Tail Soft Point
(P3006D)
  Winchester 190gr Nosler Accubond Long Range
(S3006LR)
  Barnes Vortex 168gr TTSX
(21565)
300 Winchester Magnum Hornady 200gr Precision Hunter ELD-X
(82002)
  Barnes Vortex 165gr TTSX
(21537)
  Federal 180gr Nosler Accubond
(P300WA1)
  Winchester 190gr Nosler Accubond Long Range
(S300LR)
300 Weatherby Magnum Weatherby 165gr Barnes TTSX
(B300165TTSX)
  Weatherby 180gr Barnes TTSX
(B300180TTSX)
  Weatherby 165gr Nosler Ballistic Tip
(N300165BST)
  Weatherby 180gr Nosler Accubond
(N300180ACB)
  Weatherby 180gr Hornady Spire Point
(H300180SP)
  Weatherby 180gr Nosler Partition
(N300180PT)
30-378 Weatherby Magnum Weatherby 180gr Barnes TTSX
(B303180TTSX)
  Weatherby 165gr Barnes TTSX
(B303165TTSX)
  Weatherby 180gr Hornady Interlock
(N303180IL)
 

Weatherby 180gr Nosler Ballistic Tip
(N303180BST)

  Weatherby 220gr Hornady ELD-X
(N303165BST)
338 Winchester Magnum Barnes Vortex 225gr TTSX
(21542)
  Federal 250gr Nosler Partition
(P338B2)
340 Weatherby Magnum Weatherby 225gr Barnes TTSX
(B340225TTSX)
  Weatherby 225gr Hornady Spire Point
(H340225SP)
338 Lapua Magnum Federal 250gr Sierra Matchking
(GM338LM)
  Barnes 250gr VOT-TX LRX BT
(30727)
  Hornady 270gr Precision Hunter ELD-X
(82313)
338-378 Weatherby Magnum Weatherby 225gr Barnes TTSX
(B333225TTSX)
  Weatherby 250gr Nosler Partition
(N333250PT)
375 H&H Magnum Federal Premium 300gr Nosler Partition
(P375F)
  Federal 300gr Trophy Bonded Bearclaw
(P375T3)
378 Weatherby Magnum Weatherby 270gr Barnes TSX
(B378270TSX)
  Weatherby 300gr Hornady Round Nose
(H378300RN)
416 Weatherby Magnum Weatherby 350gr Barnes TTSX
(B416350TTSX)
  Weatherby 400gr Hornady Round Nose
(H416400RN)
460 Weatherby Magnum Weatherby 450gr Barnes TSX
(B460450TSX)
  Weatherby 500gr Hornady Round Nose
(H460500RN)