Do you feel that any company has the right to charge an employee hundreds of dollars more per year for healthcare after that employee refuses to complete a yearly health assessment questionnaire?

Absolutely not. That is both extortion and a violation of privacy.

Companies have every right to request employees to complete a yearly health assessment, but they have no right to punish them with higher costs if they choose not to complete an assessment.

Yes. When an employee participates in a health assessment, it can help a company to properly fund its various healthcare programs.