I’m not a golfer, but I watch some on TV, and I see golf magazines here and there. Sometimes I hear the phrase, “Let the big dog eat.” Maybe it’s connected to those huge drivers, but I really don’t understand. Could you explain?
Its a quote from the movie “Tin Cup” where Kevin Costner uses it to mean hit the driver. The driver is generally the biggest club and is designed to hit the ball the longers.
I’m pretty sure you’ve got it. I think it refers to when you know someone is going to pull out their driver and just rip it.
I believe that this particular phrase predates the “Tin Cup” movie, as I knew what Costner meant as soon as he said it. The driver is the “big dog”, as it’s the club that hits the ball the farthest. “Letting the big dog eat” typically refers to using your driver to mash the ball as far down the fairway as you can.
(Irrelevant side note: the opponent that likes to let the big dog eat isn’t the one you have to worry about - it’s the squinty-eyed fellow who take a long look down the fairway and then pulls a two-iron out of the bag that’s the dangerous one.)
Ditto what WillGolf wrote. And keep an eye on your wallet if it’s an old two-iron with new grips. 
WillGolf is right, of course, but to some extent, the point he makes is the very point of the movie!
The championship caliber golfers aren’t necessarily the ones who pull out the big driver and go for the perfect drive. The champions are the guys who know when to play it smart and conservative.
But in “Tin Cup,” Kevin Costner’s character is a guy who’s never played it smart! He’d rather go for a really cool, impressive shot (even one that has the potential for disaster) than make the safe shot that would allow him to win.
As a result, he makes some amazing shots, but ends up out of the money, and working for peanuts at a driving range.
Yeah, but he holed 18 (really the 72nd hole) in twelve. Twelve, I say!
Well, thank you, I think. I understood a pretty good percentage of that. I feel fairly well informed, because I understood the joke about the phrase you hear on a fairway that you never hear in a bordello. Do golfers really say, “Let the big dog eat,” during play? Not in a bordello, that is.