give weight

verb2

1. •
   To attach importance to.

   • … merely observing that if you were to give weight to such an objection, there is not a panel who would not be entitled to the same benefit … — 1817
2. •
   To improve the credibility or legitimacy of.

   • What were these 250 men to come for? – I imagined it was to give weight to the petition. — 1816