Weatherald's century – the first in a BBL final – came from 58 balls and he slammed eight sixes and nine fours as the Strikers reached 202 for two to set Hobart a daunting run chase.
Travis Head added 44 from 29 while a quick-fire cameo from Colin Ingram pushed Adelaide beyond 200.
The Hurricanes were 177 for five off their 20 overs with D'Arcy Short top-scoring with 68 off 44 balls and George Bailey chipping in with 46 from 33 balls.
Veteran paceman Peter Siddle's three wickets and a containing performance from spinner Liam O'Connor (0-27 off four overs) tightened the screws on the power-hitting Hurricanes lineup to secure victory.
"I obviously dream of this, but never imagined this," Weatherald said.
"It was cool to get a century in front of my parents and play in front of such a crowd. Luckily it came off today.
"You just get that luck. A couple just cleared the boundary line, that's cricket."
Weatherald didn't pass 20 in his first seven innings in the glitzy T20 tournament, which yielded a total of 87 runs before something clicked.
He came into the final this season with three fifties in his past four innings.
Weatherald again delivered a clutch performance when it mattered most, having made 66 and 96 in his first domestic Sheffield Shield final in 2016. He also made 60 in last season's Shield final.