Your say: "His legs are quite short and he is quite chubby" to which I say the short legs are not the problem, the chubby is. Has his weight been on the increase or has the weight been stable for months?
A four year old part Terrier should be full of energy.
Our 9 year old Westie also has very short legs and he is about 2 pounds over weight (weighs upwards of 21 pounds) but he has plenty of energy. We do, however, have problems walking him on a leash. We took him in as a rescue dog a year ago and he loved to go for a walk on a leash..no longer. In his case it isn't the weight or age, it is the leash. He is a "free running" dog on our large property and he now expects to have that freedom even when off the property, he is not allowed.
Have there been any changes in your dog's life-stlyle, or continued weight gaining?
Hip problems are common in short stalky type dogs, sometimes it can be something they are born with. I would check with a vet get hip xray's!!
Obesity in dogs go hand in hand with Spinal Disc Disease......This is either a back problem or an anal gland issue....You need to see your Vet ASAP......I wouldn't wait any longer........Once you get a diagnoses, there are many preventative measures you can take.......Karla