I would suggest that the temp of a Weber grill is not sufficient to heat up a cast iron skillet to decent searing temp for 15 mins.
I use a cheap ($20) Lodge 12" cast iron skillet on my kitchen stove gas burner on the highest setting for 15 mins. Remember, cast iron is great for RETAINING heat but NOT so good heating up. You need that puppy SCREAMING hot after a good long pre-heat.
I then add just a little avocado oil (you're only lubing the skillet surface, not deep fat frying the steak) which will shimmer almost instantly.
Add your dry steak. It should audibly sizzle instantly. I sear a regular 1 1/2 to 2" steak for ONLY 45 secs on side 1, so you don't cook the interior much more, and then flip to side 2 for the same time. The crust should have a somewhat brownish tint in places. That tells me it's a good sear.
Good luck on the new cook!