For a modern airliner, wings are tested to withstand 150% of the limit load. What kind of weather would produce turbulence at 100% limit load?
The 1.5 relates to the margin between permanent bending (limit or yield load) and breaking (ultimate or breaking load).  Transport Airplanes are good to 2.5 limit load at gross weight.  Pulling more than that may or may not bend the wings permanently.  For ultimate load (pulling the wings off, it's 3.75Gs minimum using the normal 1.5 safety factor)

Those are minimums.  There is a lot of safety margin in the stress calculations so I would not be surprised at all to see an airliner take 3Gs without permanent damage even at max gross.  If the airplane is below its maximum zero fuel weight (a function of the pax and baggage load, which is where the wing bending is coming from) there is more margin, depending on how light you are.

Then there are the two speed limits to protect the structure to consider.  Maneuvering speed is the speed below which a sudden maximum elevator input will reach stalling AOA (thereby unloading the structure) before limit load is reached.  Turbulent Air Penetration Speed (TAPS) is the speed below which a theoretical worst case vertical gust will cause stalling AOA to be reached before limit load is reached.

As far as weather conditions, the biggest risk is flying into a thunderstorm cell and hitting extreme vertical gusts (mainly the up going air shaft in the center of the cell), and next to that would be Clear Air Turbulence which is usually related to crossing jet streams and passing through the shearing turbulence sometimes caused at the boundary between the jet stream and the adjacent air mass (jet streams reside in the little corner at the very top of a frontal boundary, in a little triangle of space at the top edge of the warm air mass, next to the adjacent cold air mass and the stratoshere above).  Another one is crossing rotors (spinning horizontal shafts of air) that reside below the crests of mountain waves that form downwind of mountain ranges at high altitudes.

For that eventuality you have to slow to TAPS any time you expect to hit severe turbulence like picking your way around thunderstorm cells or flying into areas where Clear Air Turbulence is reported.  In the absence of a CAT report, a cautious capt may slow to TAPS anyway if the crew notices that they are passing across a jet stream, just in case (you know you are crossing a jet when your ground speed suddenly changes and the autopilot starts making a sudden heading change to stay on track - it all goes back to normal when you leave the jet).  

In theory, staying below TAPS provides protection against permanently bending the wings same as staying below MS protects from bending the wings from a full on elevator input.  If the 777 in the incident hit 3 Gs, it suggests that they were above TAPS when it happened but even if it was fully loaded, with the fudge factor in the structural design it's not surprising it wasn't bent from an encounter only half a G above limit load.