Re: Peak voltage
Your measurements may be in error because of the significant waveform distortion at the secondary terminals of the transformer. The transformer's equivalent resistance and leakage inductance form a divider with the load presented by the charging capacitor, which is grossly non-linear. Therefore the voltage waveform is no longer sinusoidal and the crest factor no longer sqrt(2). The larger transformer has lower effective source impedance and is less affected by the non-linear load.
The distortion is particularly acute with a solid state rectifier (which has low dynamic resistance, so it ties the secondary closely to the capacitor voltage when it is forward biased) and with half-wave rectification, where the capacitor must support the entire load for over half a cycle and then be recharged in less than half a cycle, and due to imperfect coupling can push the average flux in the transformer core away from zero.
What your meter makes of both the AC measurement (of a non-sinusoid) and the DC measurement (with significant ripple) will depend on what kind of meter and whether it is true-RMS reading. Scoping the voltages would probably be quite revealing.
Half-wave rectification is usually bad for multiple reasons. One of them is to reduce the useful VA rating of the transformer well below its nameplate rating, due to the much higher losses incurred by the pulsating DC load. Is there a reason you are not using full-wave?
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