The main link between unemployment and obesity is that unemployment can cause obesity.
I've just posted about this on another thread.
The reasons why unemployment can cause obesity are:
a) Poverty means limited access to affordable healthy food and/or cooking or kitchen storage facilities.
b) Poverty can cause chronic stress - and chronic stress can cause obesity even without overeating or eating the "wrong" food. (I'll find the article I posted about this on another thread).
Separate from unemployment as in re people jobseeking (as opposed to being unable to work). Millions of people are on long NHS waiting lists. Because of delayed or misdiagnoses or delayed treatment, they're more unwell by the time they're accurately diagnosed and treated.
In the meantime many of those people waiting for good NHS care gain weight. Due to pain or limited mobility caused by their untreated health condition.
Returning to unemployment. A major problem isn't that people "don't want to work". It's that employers don't want to hire them. There's widespread employer discrimination against older, disabled - and career gap candidates. Also employers are less willing to do what they did in the past - train people on the job.
So although the weight loss drugs may be helpful for some people re obesity, they won't address "worklessness". Absolutely if it helps, they should be available to help obesity but there has to be a holistic approach - that addresses the causes (whether social/environmental or delayed NHS care).
Sort out the NHS and other public services, so there's timely access to good and holistic help.
Address poverty - with a supportive benefits system, improved child maintaince service, more council housing (bad of insecure housing harms health - at huge cost to the NHS and the wider economy), and job and training opportunities.
And address the employer problem.