Kilograms are the standard unit of mass in the metric system. Therefore, grams or milligrams can be used to get the mass of smaller objects.
I would use grams.
The unit of weight is the newton, since a weight is a force. However, when people say "weight" they often mean "mass" (or confuse weight with mass); and it is common to talk about a person's mass (or incorrectly, a person's "weight") in kilograms.
The kilogram would be logical.
The metric unit of mass is the kilogram. Why you would need to measure the mass of a necktie is beyond me.