I believe 1500HH is the minimum requirement to sit alongside any claims of being waterproof.
At a guess (I stand to be corrected) a rating of around 3000 to 4000 is probably as near to average as they come, so yes, you'll be fine for the odd shower, but don't expect it to hold out in an all night deluge!!
And remember, these ratings are a minimum "guarantee". It has probably been tested (successfully) to a fairly higher level. With your proviso of checking for "a nice weekend", I'd say don't worry about it... and enjoy!
British Standards dictate that 1500mm HH is the minimum required to be referred to as 'waterproof'. Hence 2000mm HH is plenty and conforms to British Standards.
At the risk of teaching people to suck eggs they test the waterproofing by securing a 1" tube to the material and then filling the tube with water. At the point where the water starts to leak through they take a measurement in millimetres. That is called the hydrostatic head (HH).
In your case the material started leaking at 2000mm which is about 8"...that's a heck of a lot of rain
One other thing..... new or used, it's always a good idea to not only practice pitch at home (and check all components are all there... and undamaged) but it also gives you the opportunity to either leave it out in the rain or get the hosepipe on it.... for peace of mind, mainly!
One of my favourite tents has a 2000HH rating and it has withstood everything the great British weather has ever thrown at it, including prolonged heavy rain and the odd storm!
I am sure your tent will be fine for you and your son to enjoy some wonderful camping trips together.
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