Bike weight impact on speed and commute time

I have been commuting on a aluminum roadbike that is reasonably light compared to most commuter bikes (about 20 lbs before I put my lights, saddlebag, etc on). I am planning to get a new commuter that is steel (I have to ride some rough roads/paths) and quite a bit heavier, likely 30 lbs or more by the time I put on a rack, etc.

I am wondering how much I can expect the heavier bike to slow me down and add time to my commute.

For reference, I ride a bit over 16 miles and climb ~450 feet each way, somewhat steep for some sections though most the miles are pretty flat. A few sections have a lot of lights so stop and start often.

I assume a heavier bike will have the most impact on climbing and accelerating, but not clear how much that 10-15 lbs will impact my speed and overall commute time when I factor that I weigh a lot more then the bike. I realize there are probably other factors as well, such as different gearing, etc.

Since it seems like a number of people on this forum commute on different bikes, I thought some of you may have some good insight on this.