Hi! Good question! Historically, all women were weighed as a monitoring mechanism of the healthy growth of the baby, but it was identified as a very inaccurate way of doing this and scrapped some 30-40 years ago.
As for now, the guidelines state women should be weighed at the first appointment (booking) to calculate BMI, then later in pregnancy, to identify whether there are additional factors to consider for birth (36 weeks usually - but I think in fact this often does not happen or get offered).
In terms of not monitoring weight gain all the way through, at every appointment, one simple answer is what we might actually do with that info. There are a number of different reasons for weight gain in pregnancy - fat tissue gain, baby growing, amniotic fluid, increased blood volume, placenta - but also, crucially, in the UK there are NO formal guidelines for recommended weight gain. Women often ask what is a recommended 'healthy' weight gain, and midwives often quote American Institute of Medicine (IOM) guidance, but the National Institute for Health & Clinical Excellence (NICE) here in UK assessed and rejected thos,e on the basis that we have a very different population in the UK compared to the US.
So.... we could offer to weigh women throughout, but we can't then make an evidence-based recommendation with the findings, and that fundamentally underpins the lack of weighing throughout pregnancy.