I say keep the weigh-ins exactly as they are. If a tournament decides not to offer Saturday weigh-ins on site then as is your choice attend another tournament. Myself I can't imagine having a tournament without weigh-ins just prior to each morning or afternoon session, but that's just me.
Offsight weigh-ins while sometimes necessary only encourage cheating or at least the perception of possible cheating. Friday night offsight weigh-ins only encourages parents and coaches to pull more weight on a kid. If you need Friday weigh-ins in order not to have to pull another day to make weight, then move the kid up a weight class!
All of this said, I believe the over-whelming majority of tournaments will still offer Saturday weigh-ins.