Tiny Tina should be grown up in BL3, like 20 since I'm guessing she's 12 or 13 now. She'd of course retain her zany personality (think a wacked out, explosive crazed Gaige). Her role could be one of the following:
The main villain
A siren (specializing in EXPLOSIONS!!!!!!!)
A love interest for Tannis, Lilith, Maya, or Gaige (Gearbox would totally do this)
A playable character with skills revolving around explosives and Torgue weapons.
EDIT: For a PC Tina, her action skill could be her running along dropping grenades all around her. You couldn't use guns or melee while doing this, but your movement speed would be increased by 50% (total of 150%). Dropped grenades are whatever ones you currently have equipped, but no grenade "ammo" is consumed. --- Guess who brought a jet to a gunfight?