Tenant signed a lease but wants to move in early

[Steve S.]

Current tenant moves out at the end of this month. 

New tenant signed lease for around mid August and just asked to move in 8 days early. 

They asked if they could but didn't offer to pay for those 8 days. 

On one hand, I don't have any one in there so I'm not losing any money by letting them move in. 

On the other hand, I'd be letting them stay for free to get settled in a few more days before school. 

1) what would you do?  What should I do?

2) if I let them move in early, what do I need to do about the lease here in Texas to ensure everything is legal and liabilities are covered?

Also consider that this tenant has a tad bit lower credit score than I'd prefer but pre paid a couple of months worth of rent already. 

Thoughts?  Suggestions?  Gotchas?