Why does weight loss lower blood pressure?
Weight gain increases blood pressure, the reason for this process is due to the effect of hormone called Leptin.

Leptin is made by fat and circulates in the bloodstream to reach the brain, where it acts as a signal for energy reserves, adjusting both energy expenditure and the sensation of hunger – hence it is sometimes referred to as the ‘satiety hormone’.
The group showed that some obese people who were lacking the hormone leptin because of a genetic disorder had low blood pressure despite being very heavy. This was also the case for people lacking the gene for the leptin receptor in the brain, meaning that the brain was unable to respond to the hormone.
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The team lead by Professor Michael Cowley, Monash University, Australia, in collaboration with Professor Sadaf Farooqi, from the University of Cambridge, UK suggests that the leptin signalling is necessary for obesity-induced increased blood pressure. The clinical studies in severely obese humans showed that these observations are relevant to humans.

Professor Cowley said: “High blood pressure is a well-known consequence of obesity. Our study explains the mechanism behind this link, showing that leptin, a hormone secreted by fat, increases blood pressure.”
Professor Farooqi, from the Wellcome Trust-Medical Research Council Institute of Metabolic Science added: “We now know that leptin regulates both our weight and our blood pressure through its action on the brain. Targeting this action could offer a useful way of helping people fight obesity and associated problems such as high blood pressure and heart disease.”
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It is thought that Leptin's only task is to activate the sympathetic nervous system connected to the brown fat and there by directly burns energy. But it is also behind the activation of sympathetic nervous system of heart and kidney, thereby increase the blood pressure.

Genetic and drug experiments in mice, they have pinpointed an area in the mouse brain that increases blood pressure when it is exposed to high leptin levels.
This region is called the dorsomedial hypothalamus, and is thought to be involved in controlling energy consumption. Their findings show that high levels in leptin do indeed boost blood pressure, via this brain region.

Reference
http://ndt.oxfordjournals.org/content/15/8/1115.full.pdf+html