Instant Weight Loss/Gain?

The weighing scale doesn't measure our weight $(=mg)$ , but instead just the normal reaction force between our body and the machine. Intuitively, as we bend down, the muscles in our body pulls up the lower half of the body, thus diminishing the pressure that it exerts on the scale.

We formalize this idea by considering the force diagrams. Take the downward direction as positive.
When we are standing, there is no acceleration and so $0 = ma = F = W_{\text{stand}} - N_{\text{stand}}$ which gives $W_{\text{stand}} = N_{\text{stand}}$

When we are bending down means that we are initially experiencing a downward acceleration. Thus, $0 < F = W_{\text{bend} } - N_{\text{bend} }$ . As such,

$N_{\text{bend}} < W_{\text{bend}} = W_{\text{stand}} = N_{\text{stand}}$

So the measurement decreases.

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Note: Technically, because bending lowers your center of mass, you will experience a very slightly lower acceleration due to gravity. However, in light of the Earth's radius compared to your bent height, this impact is very negligible. More accurately,

$N_{\text{bend}} << W_{\text{bend}} < W_{\text{stand}} = N_{\text{stand}}$

A weighing scale does not measure our weight independent of our state of motion, in fact just measures the force our feet applies to it. When we are at rest, the normal force from the weighing scale perfectly balances our weight so that $F_\textrm{net} = mg - N = 0 \implies N = mg$ .

As we bend down, our center of mass goes descends with overall acceleration $a$ . This can be due to several reasons. One way to think about this is for the lower half of our body, which has mass $m_\textrm{lower}$ , to remain at rest while the upper half of our body, which has mass $m_\textrm{upper} = m - m_\textrm{lower}$ enters into free fall. An object in free fall does not need to be supported by the scale and thus the scale only needs to support the weight of our lower body so that $N = m_\textrm{lower}g$ .

As $m_\textrm{lower} < m$ , by definition, we see that the normal reaction $N$ decreases as we bend down.