Hey David!
Couple takes on this:
Generically speaking, yes it often does make sense to increase your loan amount for monthly savings. As already mentioned in the responses above, figuring out your break even point (how many months it will take you) will be important for determining whether to move forward with that or not.
Question: If the rate is .625% lower and only saving you $100 net a month, what is your loan amount? The reason I ask is that certain areas like parts of VA have incentives for everyone, and if that's the case, then that 7.5% seems a bit too high. I don't know the entire situation, so that might be about par, but just my first instinct says that.
Also, as mentioned above, rates have quite literally shot back up. Considering you purchased in June and with the drastic increase in rates over the last month, everyone we are working with we are recommending to line up the refinancing: get through processing and underwriting, but don't "pull the trigger" on it until rates soften. That way you would be ready and when rates hit your target mark, you can lock it in and close right away.