The picture of the Ford above is an good example of why you have to be careful- trucks vary substantially in payload. There is a variant of the F150 which does have a surprisingly high payload. Adding heavy stuff like diesel and 4x4 eats into that payload (your 4x2 therefore gives you a weight advantage).
As has been mentioned above, get your truck with you and passengers and a full tank of gas to a weigh bridge and work out what it really weighs. Then subtract that from the GVWR on the door pillar sticker. Simplistically that will give you the amount of remaining payload. Although as has been noted above, that isn't the full story because most (or even all) of the camper's weight will be on the rear axle alone, where-as the truck manufacturer will expect some of that payload (in the form of passengers) to be in the cab so shared with the front axle.
You'll want to get uprated tyres (e.g. load range E).
I rode in a Dodge 1500 once (owned by a member of this forum) and commented on how comfortable it was. Unlike my truck the ride from the rear suspension was really smooth. He pointed out it had nice soft coil springs on the rear. So nice to drive around unladen, but probably a real handful if fitted with a camper.
The discrepancy between the "dry weight" of a camper and how much it really weighs when you use it has been noted above. So look very closely at what the camper weight sticker says, and they aren't all reliable either. They may exclude optional extras, the contents of the water tank, maybe even batteries. They will definitely exclude all the kit you take with you when camping.
As a warning, my 25 year old Shadow Cruiser states a 1400 lb dry weight. I took it to a weighbridge for the first time in June. Subtracting the published weight of my model of truck (a weight the manufacturer publishes including an estimate for the driver and a full tank of diesel), gave me a total payload weight of 2800 lbs! OK, that isn't all the camper, that is me, Sally, batteries, tools, the solar panels, safe, heavy duty replacement roof, climbing gear, a full tank of water, a portapotty and a lot of food and clothes. But that just shows how much you can go over the dry weight of the camper in real life.
If this all looks like it isn't stacking up but you still really want a truck camper, step back and think about trading the truck for a 2500 HD truck. It would probably mean spending some more money now, but you could end up spending more than that if you have to go through a series of upgrades to get the 1500 to work with a camper and then find the light weight camper you selected is too much of an accommodation compromise. I.e. you could go through a lot of effort and money and then end up upgrading anyway.
Good luck on whatever you decided to do though.
Steve.