Could I be pumping up my tyres the wrong way? I now have my first road bike. When I am pumping up the tyres with what seems like a sturdy pump (that you stand on and push with two hands), I can barely get to around 100 psi, even putting my back into it. Is this normal, or am I just weak? 

Notes: Valves are obviously presta, which I 'unscrew' and depress to let a little air out before connecting the pump.

Cheers.
I have had such experiences even at much lower pressures, (I ride diverse disciplines of mountain bike, so I use my tires around 40 PSI, but still...). I have found three main causes for inflation difficulty:

I will discard air leaks as this one is pretty obvoius.

1) Faulty valve: Some valves get somewow obstructed, and won't get air in as easily as it should. This has happen to me with three types of vaole: Schrader, Presta and Dunlop. To test for this, inflate the tube while it's off the tire. You should feel almost no resistance, since the tire is not there to build up pressure. The tube should inflate quickly. You can also try a different valve core (Dunlops are easily changeable, but not too widely used, Schraders require a special tool but are also easily changeable. Some presta valves are changeable but not all of them.

2) Pump design: Some pumps are simply, by design, not capable of much mechanic advantage, so it is harder for the operator to achieve high pressures. The force required to push down the pump's piston is the pressure in the chamber multiplied by the piston area, thus, a pump with a large area piston is harder to push, but, usually such pump will put in a bigger amount of air per stroke. As per my personal experience with a wide range of pumps, for a floor pump the best sacrifice is a pump with piston area of about one square inch (roughly one inch in diameter). It will be painfully slow for 2.5 downhill tires, but will easily pump the pressures required for road tires. (For my downhills I use a cheap pump that has a piston with 1.5 diameter, its quick, but you'd start to suffer at 45 or 50 psi).

3) (or 2.2 if wou will...) Flawed pump: This is somehow related to the previous point, but this reffers to some defect, design error, damage, wear, etc. I have used pumps that have restrictive hose, valve (almost any pump has a 'check' valve) or connector. If this is the case, sometimes these parts can be cnanged or modified, but most of the times, it's not worthy. To test for this, press the pump without anything attached. The pump should move freely, with almost zero effort and you should hear the air hissing out without restriction. In fact, you would not be able to exerpt any force donw the handle, it will quickly go down before you know it. If you can apply noticeable force, this may be the cause. This is more common with cheap pumps, but there are brands able to sell expensive ones from time to time. Restriction to air flow can also be due to debris that somehow got inside the air ducts or the valve. If the pump is serviceable with regular tools, then carefully disassemble it to check the hose, the connector and the valve or any other narrow air passages.

Naturally there are other issues tha can come up with a pump, but they are rather obvious and do not seem to be your case: such as piston seizure (It is difficult to displace the handle even as slow rate) or seal failure (gives the oposite symptom, you can not apply gerat force to the handle because the air is leaking out).

Perform some tests to discard possible causes: inflate someone else's tires with your pump, borrow a pump with different design as yours and use it on your tires. You'll easily find the culprit.