I am looking to refi and have an offer for 3.875 with closing costs rolled into the loan or 4.125 wi

IF the closing costs are truly $2500, with your loan size and a time frame of 5+ years, you will be ahead by paying the costs and getting the 3.875% rate. Those costs are quite reasonable for that loan size and rate. The only advantage of doing the free refi at 4.125% is that you always have the option (given good credit, income, and equity) of doing another refi down the road should rates drop more. That’s the #1 reason I tell my clients to avoid paying points in most cases. You’re not paying points here, and really can’t go wrong with either option. One more consideration…..if you think there’s a good chance you may be out of the house in 7-10 years, you could also look at a 7/1 arm, with rates more like 3% than your current 4% or so options.