Hi David and welcome to the forum.
Your gain in strength will be next to nothing bumping up to 1/4" thick. You will get the most gain by bumping the size of the vertical leg. For example you would double the moment of Inertia (That's a key number in determining the load carrying capability of a member) by bumping up to a 2" x 2" x 1/8" angle vs. the 1-1/2". Angle iron isn't a very good choice for a beam... especially a cantilevered beam. Also as you load it it will start to twist. Throw a gusset under the extension and you'll beef it up a lot.
Without knowing what you are doing with this... dangeling a basket of puppies over the side of a cliff vs. maybe hanging a pot of flowers off your deck... A person can only guess as to what sort of safety factor to plug into the piece. I will tell you... both a basket of puppies and a flower hanging basket will be pushing the maximum that your selection of material will handle.
When considering something like this it's a good idea to think...
"What does my gadget weigh that will be on this support?"
"Will a person ever have any remote chance of hanging off the thing along with the intended load?" (usually yes...)
"What is my total weight possible?"
"Better double that...? Triple that? (safety factor) Four times?"
"How will the load be applied?"
... And possibly several other things to take into comsideration... Then make a material selection based on the load and envelope you have to work in.
Don't want to steer you wrong and without knowing all of the conditions surrounding the situation, giving you any definite load would be ballpark at best.