Refinance advice is usually framed as a rate threshold: refinance when you can drop your rate by some number of points. That rule is too crude, because it ignores both the cost of the new loan and how long you plan to keep it.
The better test is break-even. Add up every cost of the new loan, including lender fees, title, escrow, and recording. Divide that by the monthly payment reduction. The result is the number of months you must stay in the home before the refinance has paid for itself. Beyond that point you are ahead. Before it, you are not.
Two adjustments matter. First, if you refinance a loan you are ten years into back out to a fresh 30-year term, the monthly payment falls partly because you restarted the clock, not only because the rate improved. Compare total interest over the time you expect to stay, not just the payment. Second, rolling closing costs into the balance does not make them free. It moves them into the loan, where they accrue interest.
For homeowners aged 62 and over, a reverse mortgage line of credit works differently from a forward loan and deserves its own analysis rather than a rate comparison. The unused portion of such a line grows over time under the terms of the product, and the trade-off is the balance owed against the property. It is not a decision to make from a summary.
The refinance break-even calculator at /mortgage-calculator/refinance/ runs this math with your own figures. For an independent explanation of refinance costs and the disclosures you are entitled to, the Consumer Financial Protection Bureau publishes one at consumerfinance.gov.