LTC3624 regulator won't regulate
Because it's working on no (or very light) loads it can be assumed that your problem lies in one of these areas (despite what you may think you have done): -


Input supply (12 volts) is not capable of supplying the current that the load needs - measure the input voltage when adding loads.
Inductor chosen for the design has too much series resistance - you do need to choose a decent inductor for switching applications.
Inductor core is saturating i.e. it cannot handle the current demanded by the load and is losing energy as heat.
Load resistor chosen is too low in ohms i.e. you have misinterpreted the load resistance value.