a reproductive hormone abnormality would fall under the category hypogonadism or hypergonadism. these are very broad terms, reflecting either underactive gonads or overactive gonads, respectively. This could result from any of three areas of the body: the hypothalamus, the pituitary, or the gonads. these three organs or organ sections make up what is known as the hypothalamic-pituitary-gonadal axis. therea are a number of hormones involved here. basically, the hypothalamus detects the amount of circulating hormones, sends a hormonal signal, called gonadotropin releasing hormone, to the pituitary if it thinks the body needs more (if it has enough/too much it will stop that hormonal signal. this is known as negative feedback). the pituitary will react to this hormone from the hypothalamus by sending some more hormones, leutenizing hormone and follicle stimulating hormone, into the blood. these will travel to the gonads, where they signal to make more testosterone and/or estrogen.
there could be an abnormality anywhere in these pathways. for example, if the hypothalamus is damaged then it will not send the correct signal (amount) to the pituitary, which in turn will not send the correct signal to the gonads, resulting in impaired sex hormone levels. or there could be a problem in the pituitary and so on. if the problem stems from the brain (hypothalamus/pituitary) then it is referred to secondary hypogonadism. if it stems from the gonads, then it is considered primary hypogonadism.
in contrast to a signaling pathway abnormality, there could be a problem with sex steroid metabolism. there are a number of enzymes needed in steroid metabolism, namely the aromatase enzyme, which converts testosterone to estrogen, and the 5-alpha reductase enzyme, which converts testosterone to dihydrotestosterone (DHT). there is a condition in which there is a lack of 5 alpha reductase enzyme in babies who are genetically male. they will have literally no DHT and will not develope during puberty.
as for obesity, estrogen and testosterone are the main hormones here. low testosterone can lead to accumulation of abdominal fat and this can also result from high estrogen.
This would not be a major factor, unless there was a severe deficiency. On the other hand, thyroid hormones play a large role in fat metabolism. hypothyroidism can lead to fat accumulation. In its absence (or adrenal deficiency), the body will burn less fat and this can lead to obesity.
hope this helped.