Here is an example where I have two feature classes input_1 and input_2.
Input_1 has 6 polygons - labelled with object IDs 1, 2, 3, 4, 5, 6 and colored yellow.
Input_2 also has 6 polygons - labelled with object IDs 23, 24, 25, 26, 27, 28 and colored green.
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Between them, 3 polygons from each of the inputs overlap (leaf green - 1, 3, 4 from Input_1 and 24, 27, 28 from Input_2). Thus the output will have 9 features as Input_1 OIDs 1, 3, 4 and Input_2 OIDs 24, 27, 28 are unioned into 3 features.
Each input has a field called Weight - these fields will be transferred to the output. In the output table, Input_1 (yellow) has no overlapping features (with OIDs 23, 25, 26) from Input_2 and thus has no corresponding attribute value for Weight field. As the Weight values are coming from Input_1, of the 9 output rows, these 3 rows will have 0 value (which means no value in this case).
The Weight field carried over from Input_2 to the output will be named Weight_1 (although field label will be Weight) as there cannot be two fields with same name. Input_2 has no overlap with 2, 5, 6 of Input_1 and thus no corresponding feature in the output. Weight_1 values for these 3 rows will have a value of 0 as well.