"Partial to weak hearts" isn't really accurate. The boxer breed is affected by two main heart conditions which are genetically inheritable - these are aortic stenosis and boxer cardiomyopathy. If you purchased your puppy from a reputable breeder, then your puppy's parents should have been screened for those conditions prior to being bred. The chances of your puppy inheriting such problems are thus reduced. Also, your vet should have picked up any heart murmers present when giving your pup routine examinations alongside his puppy vaccinations. If nothing has been picked up, then I don't think you need to worry unduly.
With that said, you do still need to be careful about how much exercise you give your puppy. Really, a puppy should get all the exercise it needs just from playing. Prolonged exercise can be damaging to their still-developing joints and should be avoided until your pup is around 18 months old. Taking him for walks is more about socialisation than exercise. Short walks of 20 minutes or so should be fine, but if it's longer than that you need to be careful to ensure your pup takes plenty of short rests.