Error in Magnetometer Readings

No, it's not a stupid question. Reweighting (or resampling) particles is non-trivial for any "fun" problem. Weighting is typically performed by computing the likelihood of the particle fitting the observation. See page 28 here. This link and this link give reasonable discussion on particle resampling.

These links assume you can easily compute the likelihood a particle corresponds to the observations. For ease, we typically assume the likelihood can be expressed as a normal distribution (i.e. with a mean and a variance). Since your observations are comprised multiple dimensions, you might use the multivariate version of the normal distribution.

No, you can't derive the distance to a magnet from a single field strength measurement without knowing the strength of the magnet.

However, you can derive distance from two readings at different distances from the magnet. Magnetic field strength falls off with the square of the distance. By moving a small and known amount towards or away from the magnet, you can calculate the distance to the magnet by how much the field strength changed over the know distance between the two measurements.

For example, if you moved 1 m closer to a magnet and the field strength quadrupled, then the magnet must have been 2 m away from the original measuring point. If the field strength only doubled, then you moved 1/sqrt(2) closer to the magnet. The 1 m closer was therefore .29 of the distance to the magnet, which means the magnet was 3.4 m from the original measurement.