I live in AZ, too, but I have 6 (!) rain jackets. I rarely wear them here. They are for trips and summers in the PNW.
My favorite is an old Eddie Bauer that I take to WA. But it weighs way too much (22 oz) and is too bulky to pack for travel.
I also have a much lighter Marmot (14 oz), but even using its pocket, I can't pack it down to a very small size.
This year I'm trying a very light (4 oz) and packable Land's End jacket like this one. There are also ones for men. My trip will be in June to Scandinavia with stops in Amsterdam going and coming. I hate layering, but according to the weather averages, I'll have to do it for all the places I'll be.
I have a running dialog with online vendors who say things are lightweight, but don't publish the actual garment weight or can't provide it over the phone. It's not such a big deal if you wear the item a lot, but if it stays in the bag (like that Marmot did in Italy last summer) most of the time it's a pain.
If you haven't done so yet, check the places you are going and the times you will be there for the averages. Weather2Travel is a good place to start. You can scroll down the page to get more detail, but as we all know the weather can be very different from the averages.
Not knowing how you will pack, I'm linking my other jackets that still are seeable online. I paid much less than the listed prices.
TravelSmith reversible. Mine is navy and aqua and is very old. It's a lovely packable jacket, but a little dressy for the way I pack. It weighs about 21 oz.
Eddie Bauer Mackenzie. Excellent rain and wind protection. Mine is lined, similar to this in dark smoke and weighs about 21 oz. Not easily packable, but I wore this almost every day on a May-June trip to the UK.
Campmoor Cagoule. This is packable, but makes a rather large package and is awkward to wear. I carried it on 2 trips, but didn't wear it enough to justify packing it. It weighs about 14 oz.