A base layer rated "Good" for odor resistance will easily get you through a 2–3 day ski weekend without smelling like a locker room. These are typically synthetic fabrics with an odor-control treatment (like silver-ion) or a merino-synthetic blend, and they strike a nice balance between performance and price.
The main thing to know is that by day 3 or 4, you'll probably notice some odor building up—especially after high-output skiing. If your trip stretches longer than a long weekend, you'll want a fresh base layer or access to a wash.
Also keep in mind that the odor treatments on synthetics do fade over time with washing, so that 3–4 day window may shrink as the garment ages. For a standard Friday-to-Sunday resort trip, though, "Good" odor resistance is plenty, and you'll save money compared to premium merino.