By "infants" you could mean many things. Here I assume age < 2 years.
The issues here are about accuracy of scales &c. and the design of scales &c. and how good staff are at using them. The "how" is at least as important as the equipment. Training and supervision are the key.
Scales should be accurate to +/- 50g. This is somewhat different from having a scale marked in 50g (or finer) units. Look at the manufacturers specification. There are two approaches.
(1) A scale with a "cradle" for weighing the child alone. These will be most accurate if the child is not kicking around. You may find it difficult to get scales large enough for a 2 year old. Such scales usually require a flat surface to work on. A small sheet of 20 mm plywood with wooden wedges to level it out would be useful in a survey context. a typical "baby" scale is the SECA MS-4100.
(2) Use "tared" scales. These scales take two weights and then subtract one from the other. Typically you weigh the carer with the child in their arms. You then take the child and weigh the carer alone. The weight of the child is the difference between the two weights. You can do this calculation by hand but "tared" scales do the calculation automatically. This may help reduce error. A typical "tared" scale is the Marsden MS-4102.
Remember to buy carrying cases for scales as the movements can be delicate.
For length (it will always be length in this age group) is is not really possible to measure better than to the nearest 1 mm. A design of length board that is like a trough that cradles the infant may be best. A typical length board is the O'Leary PED LB 35-107-X Infant Stadiometer.
Combined solutions are available for smaller children (e.g. < 3 months). For example, The O'Leary NWB LB 35-70-X Newborn Stadiometer is designed as a replacement cradle for an infant scale.
Accuracy and precision depends skill of the measurer. It is important that great care is used when measuring small children as it is possible to damage joints with rough handling.
NOTE : I have no financial interests in the manufacturers or distributors of the equipment mentioned in this message.