David in the future remember to never tell an applicant why they were rejected.

If there's no signs of negligence, the insurance company will reject the claim or at least counter back that the guest was responsible due to his heavy weight.

If you reject people that don't qualify and would struggle to make the rent, you are doing them a favor by rejecting them.I would have no issues with this one. 

New Testament Christians were outcast,rejects, and matyrs.

You can reuse your Zillow application for a month so there is a chance you are just getting other peoples rejects.  

I have a fear of getting rejected for loans because of my credit.

The worst that could happen is they reject your offer or refuse to talk to you.You could also offer a Master Lease, where you pay them a guaranteed $XXXX per month and then rent it to someone else for a higher price and keep the difference.

I agree with @Remington Lyman, don't give up yet on that market just because you have been rejected a few times.

, and offers three options: Tenant agrees; Tenant rejects and acknowledges they will be vacating within the period required by local law; or, they may request a compromise or other changes, which will be considered and responded to.

Viewing this background information from each tenant is a very good initial source of information to eliminate some tenants such as their rent to income ratio (3x or above is the normal rule of thumb), no prior eviction record (a prior eviction will automatically make us reject an application), and credit score (I personally do not weigh credit score when I select a tenant but others may).