The lender is taking basis risk on longer term loans since no one knows where rates will be in 15 or 30 years. The bank looks at the yield curve and prices the loan based off of a spread for 15 and 30 year product. ARMs are cheapest because they recast earlier and there isn’t as much interest rate risk in the short term.

The reason a 30 may be more interest than a 15 yr is because there is more risk that interest rates could increase during that time and the bank could be losing money at that rate vs. making a subsequent loan at higher interest. The reason that variable rates are lower is because they could follow any increasing interest rates up. I forget what the variable rate was on the free HELOC my lender gave me during a refi in 2005, but that interest rate had gone as high as 7.5% between then and the 3.75% it is now. But I also remember a time when normal mortgage interest rates were double digits, high enough that a bank offered me a discount if I paid off a 10% land contract early.

30 years takes longer to get your investment back (less on the front and more on the back of the loan). Adjustable rate the lender is hoping for the rate to be higher when it adjusts or it is set for a given time to adjust up no matter what the rate is. On a 15 year the default is lower due to being 1/2 the time.