The label on the tent will tell you how many people the tent is designed to accommodate. That is people in sleeping bags with no space to walk around and no place for anything else. My wife and I use a tent that says it sleeps 12 people. It has three rooms and we sleep in one while we can accommodate some grandchildren in another leaving the center room as a vestibule. The directions say that two people are required to set it up, but even though I am 80 years old, I can set it up and take it down alone. It has gone through several summer rains without any mishap,but I have another tent that is much smaller that I would use for camping in the snow. I have no idea what you mean by bad weather.
For two adults, their gear and a dog, I would probably want a tent at least big enough to sleep six and eight would be better. Almost any tent you find in a big box store will work for summer, even if you should have a day of rain and wind, but only if the tent is well staked and the rain fly is in place. The stakes that come withthe tents are never adequate in my estimation, I always buy at least two kinds of stakes. The ones that look like foot long nails for hard soil and the flat aluminum angled ones for soft soil or sand. The plastic ones are also good for soft soil or sand.
A tent is worth no more than you pay for it. If you buy a tent at Walmart, count your self as lucky if it is still fit to use after a year. A more durable tent is more expensive, but a better long term investment.