It can be a minor contributing factor. High estrogen can also contribute to fat storage. However, it isn't all there is to it. Even if test is low one can achieve better health and fitness, including
fat loss. I've had the test level of a postmenopausal woman for a long time and lost from 300lbs at a very high
body fat to 170lbs at a rather low one anyway with close attention to diet and exercise. Even managed to build a tiny bit of muscle in the process too. Adding weight is easier with therapy though.
Low test isn't as common as lots of us would like to believe though. If you think it may be a possibility, talk to your doc. If the symptoms are there, he or she will have you tested. The lab test costs about $150.00.
Can you be overweight with high test? Sure you can. I'm currently overweight at 205lbs with a currently "normal" test level. I'm supposed to weigh 170 so I'm 30lbs overweight according to the BMI. I'm not too fat though.
DHEA is Dehydroepiandrosterone, one of the testosterone related hormones in the body. Supplimenting with it hasn't been shown to be particularly useful except in very high dosages. I don't know how safe those high doses would be.