Define table scraps: Processed food full of HFCS, salt and preservatives or fruit and veggies and lean protein?
I think the same thing that makes dogs fat is what makes people fat: too much sugar and too much carbs. Dog treats – like Milk Bones – are very carby dog treats.
My dog is slightly overweight so my vet recommended giving her fresh veggies as treats instead of milk-bone type treats. Turns out, my dog loves carrots, broccoli, and really just about any veggie I poke in her kibble hole. She’s also a huge fan of citrus fruits, grapefruit is her favorite. I know – what dog likes grapefruit? My Florida dog, that’s who. 
This past weekend, I spotted pumpkins for pie in the produce section, so I bought a 2-pound pumpkin. And went home and just gave the whole damn thing to the dog. It took her about an hour, and I had to pick it up and scoop out the seeds & guts once she got it open, but she ate the entire damn thing. My vet has advised me to feed canned pumpkin (plain, not with the pie spices in it) for upset stomachs. So I figured fresh whole pumpkin ought to go right down, and it did. She still begged for her supper, but I gave her like a half-portion of kibble. I also switched to natural peanut butter that has no sugar added – she loves PB, but doesn’t need all that sugar.
So I try to feed myself in a healthy manner and figure, we’re both mammals, so if it’s healthy for me, it’s probably healthy for her. I try to follow the same rules for her as for me: little salt, little sugar, little fat, mostly fresh, whole fruits, veggies and lean proteins. No bones unless they are raw – once a week she gets a raw, frozen marrow bone as a treat.
She doesn’t get garlic or onions, or macadamia nuts, or raisins/grapes or any of the other things we are cautioned against feeding dogs. And she gets plenty of kibble so I’m assured she gets all the doggy nutrients she needs (no idea if Taurine is found in whole food and I know it’s not as necessary for dogs as it is for cats, but dog food has it).
See also BARF diet (Bones and Raw Foods) – some people swear by it.
Note on the begging: she has been trained if she paws me, jumps up, counter surfs, steals, or is in any way rude about getting food, she gets nothing. She sits politely and drools and then she gets the last bite or I’ll save about half a cup of rice + veggies + maybe one bite of meat for her. The garbage can latches down so she can’t open it and I do the dishes immediately to get food smells out of the kitchen asap.
I don’t feed her McD’s or anything from fast food, although she occasionally gets a french fry, it’s a rare treat. And she doesn’t get ALL the french fries. Maybe one.
Finally, anything that drops on the floor while I’m cooking is fair game. That’s her job, to keep the floor clean and to pre-rinse the dishes. 