Using all letters

                                                                            eligibility

                                                                           illegibility

                                                                            legibility

                                                                          The other words:

                                                                              beetle

                                                                               beget

                                                                             belittle

                                                                               betel

                                                                               betty

                                                                              billet

                                                                               bitte

                                                                               bitty

                                                                               elite

                                                                              eyelet

                                                                              gibbet

                                                                              giblet

                                                                               legit

                                                                              little

                                                                               telly

                                                                               tibet

                                                                              titbit

                                                                               title

                                                                              tittie

                                                                              tittle

                                                                               titty