Not just because other receivers might get jealous of that sort of attention, but because of the punishment Welker takes when he does catch the ball -- usually in traffic over the middle of the field.
But when it works, both players don't mind being a little selfish.
Welker set career highs with 15 catches for 192 yards as the Patriots topped the Jets 31-14 on Sunday at Gillette Stadium.
Welker added an 11-yard run on a reverse in the first quarter, which means with 203 yards of total offense, he accounted for just less than half of the New England offense's net yards (410).
Oh, and Welker handled four punts -- and watched a fifth go out of bounds. Busy day out there, Wes?
"It was. I knew there were probably going to be a lot of balls coming my way, but not to that extent," said Welker. "The guys did a great job around me of playing really well and blocking up front and everybody just doing their jobs. That's what it comes down to and that's how you have success out there."
While much of the pregame hype centered around the Randy Moss-Darrelle Revis matchup, no one bothered to ask the Jets how they planned to contain Welker, who was sidelined for the teams' Week 2 meeting at the Meadowlands, a 16-9 New York win.
By the time Sunday's game was over, reporters were asking Revis if maybe he should have been covering Welker instead.
"I'm not trying to point nobody out, but [with] Wes Welker, you have to press him," said Revis, who limited Moss to 34 yards on five catches. "You have to get physical with him. He's like the Energizer bunny. He keeps on going and going, even if he gets knocked down, and that's what we wanted to focus on this week. Get up in his face and make it hard for him. He's shifty in there. He's very fast and he does it week by week.
"This is a game right here where him and Brady, like I said before, it was a one-two punch in there and he was doing a lot of pivot moves and getting away and catching the ball."
Welker caught all but two passes thrown in his direction. He hauled in three passes for 51 yards in the first quarter, five passes for 88 yards in the second, two catches for 12 yards in the third, and five catches for 41 yards in the fourth.
The most jarring statistic: Welker had nearly 60 more yards receiving than the entire Jets receiving corps.
"Wow, that is pretty bad," Jets safety Kerry Rhodes said when informed of that stat, "but he is a good player."
So good the Patriots needed more than one page on their game notes to recount what Welker accomplished. Here's a quick rundown:
Welker's 15 catches were the most in franchise history for a non-overtime game. Troy Brown holds the record with 16 receptions in a 41-38 overtime win over Kansas City on Sept. 22, 2002.
Welker's 192 yards were the third-best total in Patriots history and the most ever in Foxborough. Terry Glenn had two better games, totaling 193 yards in a 23-9 win over Pittsburgh on Dec. 6, 1998, and 214 yards in a 19-7 victory over Cleveland on Oct. 3, 1999.
Welker registered eight catches for 139 yards before halftime.
It was the second time this season Welker has had more than 100 yards receiving at intermission. Welker had seven catches for 116 yards in the first half vs. Tennessee.
Welker padded his cushion as the franchise leader in games with 10-plus catches. He now has eight for his career, easily ahead of Ben Coates and Brown at five apiece.
Welker appeared ready to play 60 more minutes when he hopped up to the podium to face the media after the game. Asked if he was sore, he simply shrugged.
"Probably tomorrow," he said. "I'll feel a little bit of something and then Tuesday a little bit. But then Wednesday -- I really feel OK right now. There were a few hits in there and stuff, but for the most part, I feel all right."
It's the Jets who are really hurting. But they're not alone.
Welker has caught 79 passes for 854 yards with four touchdowns this season. Despite missing two games, he's on pace for 138 catches, which would annihilate his Patriots record of 112 receptions set in 2007 (he had 111 last year). He also could challenge the NFL record, which belongs to Marvin Harrison at 143 in 2002.
The Ravens held Welker to season lows with six catches and 48 yards.
But that probably had more to do with the fact that Welker was coming back from a knee ailment that forced him to the sidelines for the first time in his career.
Brady admitted it's nearly impossible to slow Welker, particularly when he lines up in the slot and has open field to work with -- a fact the Jets now know all too well.
"When you line up in the slot, you have the whole field to work with," said Brady. "You can go short inside, short outside, long outside, long inside, you can stop at any point and you're typically on the third [defensive back] that comes on the field.
"Wes is able to use his quickness to get open over the middle, in the flat, down the field. When you're an outside guy, you're usually against the better players and you have a really limited amount of field to work with. So if they decided to really cover you, which [Kerry] Rhodes was typically over the top of Randy and then Revis was on him -- their two best players -- then you've got to find other guys to work, and Wes really took advantage of it."
And when a receiver is as open as Welker was, you can't worry about throwing to him too often.
"I think I expect the ball to come my way every time I'm on the field," said Welker. "So I wouldn't necessarily say just because we got in the groove or anything. That's my mentality every time I step out there."
Chris Forsberg is a roving reporter for ESPNBoston.com. Follow him on Twitter.