All five Cairns starters scored in double figures.Weigh and point guard Scottie Wilbekin each tallied 16, Cameron Gliddon and Alex Loughton 11 each and Matthew Burston 10.
"The boys slugged it out tonight, we knew it was going to be a grind," Weigh said on TV network ONE.
Centre Matthew Knight was Perth's only consistent offensive threat, notching 18 points and ten boards.
Beal,who was quiet for most of the game, top-scored for Perth with 21, most of which were scored in the final quarter, but he made just seven of 20 field goal attempts.
Knight and Jesse Wagstaff both grabbed 10 rebounds, but the latter missed all nine of his field goal shots, with Perth collectively shooting just under 34 per cent.
The best-of-three finals series starts in Cairns on Friday.