Proviron/mesterolone is an analog of DHT, meaning it acts similarly in the body. Like exogenous androgens in general it can over time reduce SHBG production, which may increase free testosterone. More immediately, in binding to SHBG mesterolone can displace some testosterone, which also increases free testosterone.
Admittedly three weeks is longer than the periods in which I've experienced transition "bonuses". Nonetheless, things can still be changing out to at least two or three months. So if you want to be more sure then a longer trial is needed.