I work out six days a week. I lift upper body on the 3rd than sixth day. The other days I do cardio, balance and lower body.
Now Im 55 years of age and Im not into body building or what I'd call heavy weights.
Most of the things like 3 X10@40 for hammer curls and two handed tricep ext with 50# and dumbell bench 3x10@55. just to give you an idea. I do a lot of other lifting but with the dumbells that's the weight range. Barbells 80# lat rolls and 60 BB curls.
I do not do heavy benching or heavy squats or the like.
I do not shoot my bow the days I lift but have seen no adverse effect the day following upper body lifts.
I looked long and hard to find anything on weight lifting and shooting a bow and finally did find one article on what the USA Olympic trianer used for the American archerys and made that part of my work out.

I take it you two fellows are into some heavy lifting?