Where do you find heavy plastic grocery bags? All the bags I get from grocery stores or even hardware stores are less than paper-thin. Are you in America as I am?
I put my sleeping bag and tent into another brown garden waste bag instead of a dry bag, fold the bag over the bottom, lay it on my rear rack, and fasten it down with 3 bungee cords. Anything that I'll need to wear gets rolled tightly and then goes into zip lock bags, which I will smash as flat as possible and then zip it. I put stinky clothes rolled and also into a zip lock. Both the sleeping bag and tent came in supposedly waterproof sacks but I wiped those with the same waterproof Nixwax stuff I use on the tent using several coats, I'm pretty sure the brown yard trash bag works the best at keeping water out. Neither the tent nor the sleeping bag got damp in torrential rain storms I've been in.
My panniers, so far after 4 seasons and two torrential rains, I mean rain so bad and so long one of them overflowed a river that went over the top of a bridge on a minor road and they had it closed off, so I had to take a 5-mile detour. I was riding in that crap, and hated it, but it was hot out when that was happening so I didn't put on my rain pants or rain jacket, just a waterproof helmet cover, so I was soaked, it was so hot that when it stopped raining a couple of hours later I was dry in about 10 minutes! but I digress, not a single drop of water got into either of my panniers, not even when I pulled the brown garbage bags out to check to see if water got into the panniers, nothing, wasn't even damp. My handlebar bag was soaked inside, even with the rain-fly on, but due to me using a white trash bag as a liner, no water made it past that and into my stuff.
Those rains were so bad I seriously doubt if that had happened at night I would have been able to remain dry. Tents do wet through if too much water gets on the fabric. I put 5 or 6 coats of Nixwax on my tent and rain fly, I have slept in minor rain inside that tent but not something major, so not sure how well the fabric would have held up with the Nixwax treatment under torrential conditions. The reason I put so many coats on is that while the instructions say just one coat is needed, the fabric felt like nothing was on it, after I got done with all those coats, it now has a waxy feeling to it. All I need to do before every season is put on a single coat as long as I can feel it on the fabric.
My panners are Axiom Monsoon Oceanweave 45L panniers I got on sale for half-off 4 years ago. They don't come with rain-flys because Axiom said they're not needed, but they do make them so I bought a yellow pair, I bought those because the color heightens visibility over the gray-black color of the bags, and the flys will help prevent abrasion wear and keep crud off the bags so all I have to do is rinse off the flys if they get cruddy. I do treat the flys with waterproofing spray because when it comes to water getting in I get a bit paranoid! LOL!! I did test one of the bags by using a garden hose on full force all over the sides and tops of the bag for about 10 minutes without a fly-on, and no water got in, so I think the bags are watertight without the flys, but the flys were cheap so I got them mostly to keep the panniers looking good and visibility.
I always try to talk to other bicycle (or backpackers) tourists/campers whenever I run into them to pick their brains, and they pick mine, it's a long learning process, and what might work for one person another person may not like the idea, which is fine, everyone is different. For example, I take a 3-panel solar panel to keep my stuff charged, some people I run into don't, they just wait to get someplace they can plug everything in, I rather not have to hunt for an outlet, or stop for a couple of hours someplace to charge, but that's me. With that solar panel, I can even charge something while riding, it just gets strapped to the front rack and I plug something in, usually the phone when I'm riding, I need the lights as I ride and charge those and the GPS after I get to camp, I carry a very thin lightweight power bank in case there is no sun. On my first couple of trips I carried a very cheap stove and a separate windshield, one of the other people I ran into used a Solo Windmaster and said he didn't need a windshield with it, so when I got home I ordered one and now I no longer carry the windshield which saved me a little weight and wind doesn't bother it much, not to mention the Solo Windmaster works better than the cheap $12 one I originally bought.