I'm a physiotherapy student and have done a fair amount of exercise physiology in the last few years so I may be able to shed some light on the situation (hopefully in laymans terms).
A Brief introduction to Exercise Physiology of Walking and the relationship between Oxygen Consumption, Energy and SpeedWhen walking across level flat ground, speed and metabolic costs (energy costs) have a sort of parabolic relationship (no quite - but its important to note that it is certainly not linear). When walking as slow as possible you use energy to power muscles to resist the swing of your legs that naturally occurs when walking due to gravity. As you walk faster (or move into a jog/run) you power muscles (in a different manner) to propell your legs faster therefore your energy costs are going to rise. Optimal conservation of energy is going to vary a little bit between each individual but is usually balanced on the slower side of things (around 2-3km/h).
Your normal speed of walking (i.e. if your not making a concious effort to move quickly) is usually around the most energy economic way to walk. Out bodies are designed/developed over many years to move in a manner which is most energy efficient. Of course putting additional weight on your back and changing torrein is going to increase energy costs, however, the principles behind the energy-speed relationship are going to remain the same.
Where the differences come with walking uphill/adding weight to your back is that you are doing more work which requires more energy production which in turn requires more oxygen. If you have insufficient oxygen supply to the muscles (possibly because you aren't 'fit' enough) then your body will have to create energy by a different metabolic pathway (one which doesnt require Oxygen but is alot less efficient and has by-product of lactic acid). It will, as mentioned above, look to burn different fuels in order to get the oxygen - one of which is glucosen which can be readily taken from the bodies glycogen stores (instead of using up all the fat we all want to get rid of). Our stores of glycogen are alot smaller than that of fat, so once you have used it up your going to start feeling tired.
So in summary walking faster >>>> lack of oxygen to muscles (even in fit people especially once walking much faster) >>>> uses different metabolic pathways to get energy >>>> uses fuels that we have less off >>>> we run out faster >>>> feel tired (and want to eat) believe I read somewhere that if your body runs out of carbs or water you have to slow down as you have to burn your stored fats which are much slower at being converted to energy than carbs???
at lowest possible power outputs 80% of your fuel comes from fats at the highest you can achieve 100% comes from carbs. If you want to burn fat at a maximum rate you need to work at around 65% of your maximum oxidative consumption possible (VO2 max) [which is more or less your maximum work output as work and VO2 are linearly related]
A good test for this is called the talk test (as tasman described above) - at the point in which you can no longer hold a conversation while exercising you using around 60-70% of your maximum oxygen consumption.
(this can also be estimated by using a formula that takes into account your maximum and resting heart rates)
The stiffness I assume you are talking about is delayed onset of muscle soreness (DOMs) and is worst 48hours after exercise? The scientific jury is still out on why this is caused.
One theory is that it is caused by lactic acid build up (although there are a number of mechanisms not explained by this theory). Lactic acid is a by product of using a metabolism pathway that doesnt require oxygen (used as a result of lack of oxygen in the muscles). As you increase your work (i.e. walk faster) if your ventilatory system can't keep up you are going to produce more lactic acid (due to burning different fuels) which will lead to more soreness (however, lactic acid has been shown to leave the muscles quite quickly - therefore it could be argued that it doesn't cause DOMs which are felt worst 48h after the event).
A more recent theory is that it is due to microtears in your muscle. They believe this occurs more when your muscles are used eccentrically (contract in manner that they lengthen rather than get shorter - I can give a better explanation if needed). Muscles are often used eccentrically to slow body parts down or to lower your body weight (explains why muscles are often so sore when you have been going downhill all day). So if for example you are swinging your legs faster during walking some of your muscles are going to have to work harder to slow the swing of the leg just before you place it on the ground. These harder working (eccentrically) muscles are more likely to get micro tears.
I Hope that made sense to the people which could be bothered to read it - If anyone has any questions just ask.