If it took 2 or 3 weeks to drain, the current flow is well under 1 amp.
Assuming your battery has an amp-hour capacity of 60 (just a guess) the current draw from whatever is causing it to run down is estimated around 150-200 mA (60 A-hr/336 hr = 0.18 A).
This should be easy to measure with your meter and there should be no risk of blowing the meter's fuse if you get it replaced.
That is not a lot of current, but enough that it could be almost anything. It could be a short in a lighting circuit, a leak through corrosion products at your fuse block, or even a powered load (like a light bulb) caused by a wiring error or failed switch.
Mike
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