It's normal to see a boost converter's voltage drop when you connect it to the load.
To understand switch-mode power supplies, it helps to think of the output capacitor as a rechargeable battery and everything else as the charger.
If we expand the timescale and replace the output capacitor with an actual battery, the system mechanics stay pretty much the same. As you draw power from the battery, its voltage drops. If you draw a lot of power, it drains quickly. If you only draw a little power, it drains slowly. If you connect a charger that comes on, say, once per day, the battery will start with a full charge every 24 hours.
If you graph the battery voltage, you'll see a series of rising and falling curves.
The rising parts of the curve occur when the charger is on. The slope of the curve will depend on the difference between the power the charger can supply and the power the load wants to draw. If the charger provides a lot more power than the load wants to draw, the battery will charge quickly. If the charger only supplies a little more power than the load wants to draw, the battery will charge slowly.
The falling parts of the curve occur when the charger is off. This time, the slope just depends on the amount of power the load wants to draw. More draw gives you a steeper curve, less draw gives you a flatter curve.
If you connected a very slow-moving voltmeter to that circuit, it would show you the average of those curves across the whole cycle. If you didn't connect anything but the VOM, you'd see a high voltage because the VOM doesn't draw much power. If you also connected a load that draws lots of power, you'd see a lower average voltage from the steeper charging and discharging curves.
A switch-mode power supply works pretty much the same way, but the charge/discharge cycles are on the order of kilohertz or megahertz, not cycles per day. The difference between the high and low points of the charge/discharge curve is called 'ripple', and should be within a calculated range if your converter is working correctly.
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