Hello,
Background verification procedure changes from company to company. You can ask for the professional references (at least 2) from the candidates at the time of interview. Upon finalizing that candidate, check with those professional references on what they think about his candidature.
Professional references can be ex-boss, ex-senior colleagues etc. from whom we can obtain authentic information and working experience with that person.
Keep the record of what questions did you ask them and the answers received.
With regard to the specific answer to should we do background verification for 7+ years experience or not ? - I think we should do it as a procedure. It will not only help you assess his candidature but also give you a chance to check his leadership, supervisory skills, maturity, team skills etc. if he is going to join on a higher / senior position.
Hope you got your answer.