Professional singer here.
When performing the Valsalva while lifting, the vocal folds form a seal, resulting in a closed glottis. You do the same thing when you cough (very short), sneeze (a little longer), poop (even longer), etc. As long as you don't audibly grunt or groan while under load, there will be absolutely zero detrimental effects on your vocal folds.
I don't have any scientific evidence to support this, but I believe weight training has actually improved my singing. It may be that since the thorax is engaged when performing the valsalva, the laryngeal musculature is thereby strengthened. Before beginning weight training, I struggled with F above middle C. Three years later, I have an effortless F, a comfortable F#, and even a G on my best days.