It may be more convenient to use MolarMass (Kg/mol), rather than AtomicWeight (Kg), and do the calculation as the OP suggests.

ElementData["Tin", "MolarMass"] / Quantity["AvogadroConstant"] // UnitConvert

1.97123 × 10^-25 kg

To calculate the mass of one tin atom as the OP suggests, it is probably more convenient to obtain the Molar Mass, and then divide by the Avogadro constant.

ElementData["Tin", "MolarMass"] / Quantity["AvogadroConstant"] // UnitConvert

1.97123 × 10^-25 kg

The default output for MolarMass is (conveniently) g.mol^-1 (rather than Kg.mol^-1)

ElementData["Tin", "MolarMass"]

118.710g/mol

Mathematica (apparently) makes no distinction between AtomicWeight and AtomicMass (IUPAC discussion), (the default output (v11) is unified atomic mass units, u), and the result the OP requires may also be obtained as follows:

ElementData["Tin", #] & /@ {"AtomicWeight",  "AtomicMass"} // UnitConvert

{1.97123 × 10^-25 kg, 1.97123 × 10^-25 kg}

Although the default output for MolarMass is g.mol^-1, Mathematica is clever enough to evaluate the following as true

(ElementData["Tin", "MolarMass"]/Quantity["AvogadroConstant"]) == 
ElementData["Tin", "AtomicWeight"]

True