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The former Welsh Guard, who was badly burned on the troop ship Sir Galahad in the 1982 war, signed up at aged 16.
More than 1,500 forces personnel will lose their jobs in a fourth and final round of recent redundancies.
The MoD said Wales remains a key recruiting ground, with plans in place to recruit 1,000 young people annually.
A spokesman declined to comment on Mr Weston's statement.
Defence Secretary Philip Hammond announced the final round of armed forces job cuts since the 2010 defence review.
He said 1,425 posts will come from the Army, 70 from the RAF and 10 from the Royal Navy.
The fourth tranche of redundancies is part of an armed forces re-structuring programme which will see the regular Army cut from 102,000 to 82,000 by 2020, while the newly-renamed Army Reserve - formerly the Territorial Army - is being expanded from 19,000 to 30,000.
When asked by BBC News whether he would join up in the wake of the current defence post cuts if he were a youngster, Mr Weston, who grew up in Nelson, Caerphilly county, said: "As a 16-year-old, if I knew then what I know now, probably not.
"I look at it now and I think 'is it worth going in?'
"No, I probably wouldn't [sign up]. I'd think that it's risk just not worth taking."
The Welsh Guards are now based at RAF St Athan in the Vale of Glamorgan.
Other regiments that traditionally recruit from Wales include the Queen's Dragoon Guards, known as the Welsh Cavalry, and the infantry regiment, The Royal Welsh.
With about 5% of the UK population, Wales regularly supplies up to 7% of new Army recruits.
The Army is one of the largest employers in Wales, with around 5,000 soldiers based in Wales and 8,000 from Wales based elsewhere.
Despite redundancies in the armed forces, the Military Preparation College aims to recruit at least 1,000 young people from Wales each year.
A Ministry of Defence spokesman said: "Wales has been and continues be a key recruiting ground for the armed forces."
Post reductions in the latest review will be not decided by location so it would not be possible to say how regiments that recruit in Wales would be affected, the MoD added.