Come to the Margolis Market Information Lab (MIL) at the Business Instructional Facility (BIF) and use Bloomberg.
Type the company ticker symbol. Hit the yellow Equity key; and type WGT.
Example: IBM [EQUITY] WGT
You will see the indices in which your company is a member.

For information on a particular index, select it and type DES (for a description of the index, its constituent members, and its pricing, etc.).