Official FAQ wrote:
Heavy Weapon
Q: Characters with Heavy Weapon can't attack and move in the same turn. How does this work with ASP-7's Lift ability? Lift "replaces attacks," so can ASP-7 move another character with Lift and also move that turn? Can it use Industrial Repair on another character and still move that turn?
A: Yes. Abilities that replace attacks don't count as attacks themselves. So ASP-7 can use its Lift ability and also move, or use Industrial Repair and move. Heavy Weapon only prevents it from attacking and moving on the same turn. A character with Heavy Weapon can still make an attack of opportunity as normal, and it can move in the same turn that it uses a replaces attacks ability.