Well now you've got me there: I've never been at 300 lbs.
I agree it makes sense to research a bike purchase to assure the particular bike will support the anticipated load. At the same time, some of us started out overloading the equipment and just had to work to get to a "within specs" weight.
LiveStrong puts the max weight for a Huffy 26" bike at 250 lbs. The iconoclastic Huffy's are duplicated in much of what we see today in the department stores. No, they are not high-line LBS bikes, but they will get the job done until one can afford something else.
So if the OP's fiance wants to go that route, he can inflate the tires to the max psi and look for his weight to come down as he gets into shape.
I think a more pressing issue than the tires and spokes may be the overall fit and the safe extension of the seatpost at his 6'3" height.
For example, Cannondale's road bike sizing chart puts a 6'3" rider on a bike with a 60 cm (23.6 inch) seat tube. Their mountain bike chart puts the same rider on an extra-large (22 inch) seat tube. The Giant OCR series chart shows a size exactly the same as the Cannondale. Their other charts vary a bit.
The upshot is that with a bit of checking and a tape measure, he can know if what he is looking at is in the ball park in terms of size and fit. After that, he has to do the work to get his BMI down into the acceptable range.
Back to the weight issues, using the BMI calculater at the link, I found that he has to lose 100 lbs to get into a normal BMI range.
Height 6'3"
At 300 lbs BMI of 37.5 (obese)
At 275 lbs BMI of 34.4 (obese)
At 250 lbs BMI of 31.2 (obese)
At 240 lbs BMI of 30.0 (overweight)
At 230 lbs BMI of 28.7 (overweight)
At 220 lbs BMI of 27.5 (overweight)
At 210 lbs BMI of 26.2 (overweight)
At 200 lbs BMI of 25.0 (normal)
The link:
https://www.nhlbi.nih.gov/health/edu...MI/bmicalc.htm
At 200 lbs the whole discussion becomes moot.
I'm just saying...