Is there any swelling at any of the joints or leg?
Where on the leg does he experience tenderness? (Feel the entire leg for signs of tenderness)
When it starts up after stopping is there anything that triggers it to start again?
It sounds like he may have pulled a muscle but there is always the possibility that there was a injury to his ACL. I doubt it was a rip since he can get up on it for a while. The bad news about injury's to the ACL is it takes a great deal of time to heal.
You can take him to your vet for a xray (Which is what is recommended) but if this is simply not what you want to do, then you can treat it as a injury to the ACL and do home therapy.
Basically you have to keep him off of his feet for at least a few weeks, limit his exercise by only allowing him outside for bathroom breaks and only on a leash to keep him from running. These should be very short breaks (Around 5 minutes) The key to healing a injury such as this is to either have it surgically repaired or do complete bed rest.....which is not always easy.
Most owners find using a kennel or crate works well. I prefer using a small room such as the bathroom with baby gates put up to keep him in there. This limits the area he can move around in and allows the ACL to heal better. You can use Warm compresses on the leg to help with any pain he may have as well. Extra blankets for him to lay in is recommended. This helps him get comfortable without to much pressure on the leg.
It is recommended that you start out with 2-3 full weeks of bed rest, no activity other then bathroom breaks. After that he can take small walks and come out of the bathroom (Or kennel) for the better part of the day as long as you can supervise him and make sure he is not running or jumping on anything. It will take a full 5-6 weeks to heal this injury.....thus no running, jumping, excessive exercise etc for the full amount of time. As the leg gets stronger you can increase his walks to longer periods but avoid running and jumping completely for the full 6 weeks.
Now, with this limited activity weight gain can occur, so make sure you are not feeding extra snacks. You may also want to add some veggies to his diet. If you notice increase in weight you can switch him to a "Lite" food for the duration of his heal time but as long as you take it easy on the snacks it should not pose any real problems.