Brightness really matters for outdoor setups, and you're looking at needing something in the 1000-1500 lumen range minimum if you want usable picture quality before full darkness kicks in. Most portable projectors advertise way higher numbers but those are peak specs under ideal conditions. I picked up a mid-range one last summer and learned the hard way that 500 lumens sounds fine until you're actually trying to watch something at dusk with ambient light still around.
The weight-to-performance balance tends to favor something between 2-4 pounds rather than the ultra-light stuff that often sacrifices brightness. You'll also want to think about throw distance - where your backyard sits relative to where you can mount or position the projector. If you've got decent space, you've got more flexibility. The real game changer though is getting a proper portable screen instead of relying on a sheet or white wall, because that actually amplifies brightness perception and picture quality matters way more than people think once you're sitting outside watching something.
Battery life is another practical consideration if you don't want to run power cables everywhere. Some projectors handle 2-3 hours unplugged which is solid for a movie night or two, while others need constant power. Factor in that outdoor movie nights often run past sunset into the evening, so you might want something you can keep plugged in anyway. Test any projector indoors first if possible to see how it actually performs in semi-lit conditions before committing - specs look great on paper but real-world backyard use is pretty different from a dark living room.