Donkey Kong is an absolutely fantastic (and underrated/underused) character, one that, at the top level, will probably be even for GW.
His Advantages:
Weight - DK is one of the top three heaviest characters in the game. He will be able to kill you at 60%, while an uncharged fsmash probably won't kill him at 100% with proper DI. He will often live up to 160% while you attempt to get a kill, and by that time he can get several stocks off on you.
Strength - This isn't as obvious as you would think. GW has absurdly good smashes - range, strength, disjointed hitboxes (except for usmash), and good speed in proportion to their power. DK might be one of the few other characters in the game with smashes just as good - if not better (I think they're better) - than GW. Each one of his smashes uncharged will kill at around 70%. Each one has absurd range because of the length of his arms. Each one, I believe, is the same speed or a bit faster than GW. Point blank - at close range, with both people attempting to Smash, DK will probably kill GW. The matchup requires just as much spacing, I think, as against a good Snake with this in mind.
Recovery - Before you say "Wtf, DK's recovery sucks...", think about a few things. DK has one of the best horizontal recoveries in the game, but he has one of the worst vertical recoveries. Against GW, however, this doesn't really matter - GW doesn't have KO moves that kill by sending downwards in a hard-to-recover area. He either kills up (usmash, SS'd dsmash) or up and to the side (fsmash, fair). The one move that's different - non-SS'd dsmash - can still be recovered easily by DK's horizontal recover. Edgeguarding DK is decently easy, but his weight and constantly damaging up-B make it near-impossible to get an early - or even late (before 110%) - kill. Basically: DK is going to live for a long time while he can kill you without a lot of work.
Ground Range - DK's tillts are incredible. His dtilt is good for spamming and has range, his ftilt has MASSIVE range with good priority and damage, and his utilt is excellent for juggling to set up into his awesome uair. I *think* his ftilt has more range than GW's dtilt, but even then, it's extremely hard to space a good DK on the ground. If you're just out of his tilt range, he can still down-B to start aerial juggling.
DK's Danger Zone: You have a big disadvantage on the ground in the area where DK's ftilt goes to a little behind him (where the smaller hitbox of his dsmash is). He can kill you easily and rack up a lot of damage. You have a disadvantage directly over him (his utilt) and a very tiny space above that (where he can uair you before you dair). In the air, you don't want to be near him while his back is facing you. His bair's got range, speed, power, and no lag.
GW's Advantages:
Size - This is a lot bigger than you will think. DK will approach in one of two main ways: tilts or bair. One of DK's biggest disadvantages is the fact that his approach is limited to bair, but, luckily enough for him, it's definitely his best move in his arsenal. Double bairs from DK are great for approaching opponents on the ground, but they're difficult/less effective against smaller characters. It's harder to hit, and DK has to land while using the move while still close to the ground. Against smaller characters, DK normally has to limit his bair approach on a grounded opponent -- this means he's probably mainly sticking to tilts, which are beatable.
Aerials - DK's got some decent aerials, but they're nothing compared to GW's. DK's bair is f'ing incredible, but GW beats or at least rivals it with the turtle. DK's only other great aerial is uair, which GW easily beats with dair. His fair and dair have big problems: slow, predictable, and very easy to punish. GW has range and disjointed hitboxes on his aerials, which means that DK will probably not try to approach via the air as much if not at all. Basically, GW will try to stay airborne while DK will try to stay on the ground.
Speed - DK is alarmingly fast for his size, which could throw off a lot of GW players. Don't be put off by it, though -- GW is faster. All of his air moves come out incredibly quickly with great range. Nair and bair have very little landing lag. DK can and will overpower you, but the trick to playing against him is to hit and run with your better aerials until you can get a kill.
Air Range - This is mostly explained in aerials, but it's worth repeating. GW can rack a lot of damage on DK with little risk. When DK's off the edge, he will, in all likelihood, get back. However, GW can still interrupt the recovery for a good while by avoiding DK's damaging up-B with disjointed hitboxes on fair and bair. Disjointed hitboxes are huge because, for a good amount of the time, you can approach and retreat if your attack pings with his without taking damage.
GW's Danger Zone: Basically, anywhere in the air is dangerous for DK. His worst situation with you is above you. His dair is way too slow with a small hitbox to faze you, and his only option is really either airdodging (predictable) or fast-falling a nair (small hitbox, little priority). If he's facing you in the air, he's in trouble. He's also in danger if you're above him. Your dair > his uair. Basically, GW is more dangerous anywhere in the air except where DK has his back turned to you, and then it's mostly even.
General Strategies:
Strap your goggles on, son, because you're going to the air.
DK doesn't take kindly to people who try to approach him on the ground. He's got too much power, too much range, and too much speed. If you try shielding, DK's got one of the better grabbing games in Smash with his cargo throw to set up a myriad of situations, all of which could potentially screw you.
Bair remains an amazing approach for a grounded DK, and, to be honest, you should be use it to the point of spamming. His size means he's pretty susceptable to the turtle's range, and he can be shieldpoked easily. It comes out fast, it racks up damage, it loves bigger targets, and the last hit pops him out and above you - right where you want him. If DK is staying on the ground, which he probably will, resort to your safest, most effective approach: bair that simian until he decides to get his banana-loving behind off the ground.
Dair is a good approach too, but it's a bit predictable. I also think he can connect with a usmash (killing you at some absurdly low percent) while you do it. Fair is normally good in most matchups, but with DK a whiffed fair means that he will probably kill you above 65% with a fsmash while you're in landing lag. Since DK has so much potential to punish in such a big area, you've gotta be as safe as possible.
Basically: the best place you want to keep DK is above you in the air. Nair destroys him with it's hitbox size and his character size. Uair juggling can set up for the occasional usmash for a ton of damage. He's got very little offensive options in the air except bair on you, so abuse him and rack up as much damage as possible while he's airborne. You know that most of the time he's going to airdodge, so predict and punish with one of your smashes.
GW's recovery makes it hard for DK to pull off his early kill moves (Cargo Stage Spike, dair, fair), but it doesn't matter as much because GW's weight makes him die so early with smashes.
One last thing: know that DK, like GW, can rack up damage without you really even realizing it. A triple bair combo or a bunch of stringed tilts will put you at 40%. GW has the same ability with his arsenal, but the difference is, DK only needs two strings of combos to put you in the kill-zone, while you need 4-6.
Matchup Rating:
This matchup would be in GW's favor by just matching each character's movesets. However, when you consider weights, I highly doubt this is in GW's favor. So, I'd give the matchup:
5/5
