Mint, little pups - so from newborn to 8-12 weeks tend to be little pudges, then they lean out as they grow. When their testosterone kicks in they tend to go skinny and gangly, a bit like spotty great human teenagers really.
In my experience they tend to fill out a little, then suddenly drop weight and go skinny as they have a growth spurt. Then as they start to develop an adult shape and size their muscles build and they loose the half-starved look.
Dogs are meant to be lean, you should be able to clearly see their waist from above and their ribcage should have a lean covering. The vast majority of dogs these days are overweight and it's what's been implicated in all sorts of health problems from hip and elbow dysplasia to diabetes and some cancers.
The guide for a healthy Lurcher is that you should be able to see the last three ribcages. Pip is extremely thin, but fits that description. Lurcherboy has put on too much weight recently (2kg!
) mainly due to less off-lead exercise while dh was walking him and is now on a diet as a result.
Your Whippet x Collie was a Lurcher!
Lurcher = any sighthound x any working breed or terrier. 
Re treats, I have 2 x fist sized bags with me, for two dogs, plus a couple of catfood trays in case I want to jackpot recalls. I usually get through one bag on an average walk, maybe with just a few bits left - but - if it's a busy walk with lots of other dogs, I can get through two whilst shoving treats down Pip's neck for counter-conditioning purposes.
I use, fresh cooked chicken, chorizo, cheese, primula, fish4dogs stars, kibble and catfood trays. I've just bought some chorizo cocktail sausages and for some reason my two go nuts over those, far more than proper chorizo. The best puppy-crack training treat I've ever used was Morrison's turkey sausages. They were really greasy and smelly and worked like a charm, but they don't seem to sell them down here.
Not all dogs are food orientated though and for those dogs I'd get them hooked on 3 A, B, C graded toy rewards that they only get as a reward for training/good responses.
Lurcherboy is food oriented, but tennis balls trump everything else on the planet, so I can use both with him. For Oldgirl, who was a total glutton, her frisbee still overrode food when out on walks.