I certainly would be looking for another vet if I were in your shoes. Heart murmurs are graded on a level of 6 and the only thing a specific grade indicates is the level of sound. Low grade heart murmurs are not unusual in young puppies (and even in humans). I just fostered a litter of 6 puppies where 2 had heart murmurs (heard at 6 weeks). One was a 1/6 and the other a 2/6. Within 3 weeks following, no murmurs were detected. These are what's known as "innocent murmurs" as Aslan has described. The only way a vet can detect if it's a serious heart condition is through a cardiac ultrasound. I can't believe the one you saw said it can go from 1 to a 4 without justifying why he thought so. And then correlating it with your puppy's limp without any further testing
? Seriously, I'd be looking for another vet.