As with most things, reality is probably somewhere in between. A 5% energy expenditure increase for a 1% weight increase seems high: if that were true I think it would be a lot easier to lose body fat. I'm about 10% higher than my "racing weight" of a few years ago but I know that I'm not eating 50% more calories just to maintain equilibrium. If you really want to geek out on this I found a paper describing metabolic cost of weight on ankles, knees, and back that puts numbers to the well-known extra penalty of boot weight:

http://www.bgu.ac.il/~rriemer/papers/Schetzer%20Riemer%202014%20Metabolic%20rate%20of%20carrying%20added%20mass%20A%20function%20of%20walking%20speed,%20carried%20mass%20and%20mass%20location4.pdf

They seem to confirm prior work indicating a linear relationship for weight held close to the core and increased penalty at the extremities. They also measured O2 consumption with a mask, which has to be much better than my cheap HRM.