That's an interesting problem. Most plastic boxes are not watertight. The ones that are can be expensive, as you already know. I don't know what kind of items you're storing. You might have to settle for using big plastic bags inside the totes and of course the bags will have to be tightly closed with no rips or holes anywhere. Those big contractor garbage bags are pretty tough and they're large. If it's food you're storing, you might even double bag it.
The other problem is that not all plastic boxes are proof against UV light, which they will get if they are stored outside in sunlight. I used one as a planter and it got very brittle by the end of the second year. Putting a tarp over them could help with that, and usually a box that's black will be much more UV resistant than one that isn't.
Several thoughts here. There's a place called Uline that sells industrial supplies online. They have industrial grade stuff, intended for storing and shipping. They sell plastic barrels, up to and including ones the size of an oil barrel. They also have those plastic totes with the flip lids, those are called Round Trip totes. On the cheaper versions of those the lids tend to warp if you stack and the box isn't full enough to support the lid but industrial grade ones will be better that way. They have plastic buckets, the kind that they sell 5 gallons of paint in. Lots of good stuff on that site. I've bought stuff from them and service was excellent.
The best overall "cheaper" plastic box I know, and trust me, I've tried most of them, is made by Sterilite but you can no longer find this particular kind in Wal-mart and stores like that. You can only get them from The Container Store. Lucky you, there are 3 stores in the Houston area. http://www.thecontainerstore.com/shop?productId=10021311&N=Ntt=sterilite
I've been using those Sterilite containers for many years, bought the first ones over 15 years ago and the only ones that got any damage so far were ones that took an impact(such as when I threw my two-way radio at it in a temper), and one where a dog chewed the lid. I used to use them at work, storing tools and hardware in them, taking them to job sites. I can stack them at least 4 high with that kind of stuff in them and they do not collapse. I can stand on the top of one and the lid won't give way, and I have used them as stepstools many times. I weigh about 140 lbs. The lids are secure enough that you can pick them up by one end and carry them without things falling out. I like them so much that I have made a special trip into the US to buy more, back before they shipped to Canada.
They come in white and in black. If UV exposure is a concern, I'd go for black, but the white ones have the advantage of making it easy to see what's inside if there isn't much light. Or call Sterilite and ask if they are UV resistant.