Sunny weather doubles the restorative power of those moves. And Link Battles will assume the time of day is whatever is most beneficial to the move. Since Synthesis, for example, heals 50% under normal conditions during the day (25% otherwise), it will heal 100% in sun during the day (50% otherwise), and the link battle will assume it's day. Moonlight is the same - heals 50% under normal conditions at night (25% otherwise), heals 100% in sun at night (50% otherwise), and the link battle assumes it's night. Rain is the opposite - cuts the restore rate in half, so Synthesis would only recover 25% (12.5% if it wasn't a Link Battle and it wasn't daytime).