Let's look at the examples in Mundane Beasts:
gyrfalcon: -3 & roughly 1.18-2.1 kg
other falcons: -4 & (Eurasian hobbies are around 0.175-0.285 kg; Eurasian kestrels are around 0.163-0.29 kg; male peregrines are around 0.424-0.75 kg while females are around 0.91-1.5 kg; male lanner falcons are around 0.5-0.6 kg while females are around 0.7-0.9 kg)
So by mass/weight we would think size -4 is around 2 kg and size -5 is around 0.5 kg (1 kg if the authors were just considering peregrines, lanner falcons, and the like. Now let's look at the size examples from ArM5.
size -3: baby (it doesn't specify at birth, so I'll go with the upper end of average at birth to account for a little time afterward, meaning about 4 kg)
size -5: rabbit (0.4-2 kg)
size -10: mouse (around 0.02 kg)
So we have a fair amount of agreement if we go by something like this:
Size 0: 60 kg
Size -1: 30 kg
Size -2: 15 kg
Size -3: 5 kg
Size -4: 2 kg
Size -5: 1 kg
Size -6: 500 g
Size -7: 200 g
Size -8: 100 g
Size -9: 40 g
Size -10: 20 g
This is roughly a multiplication of 2 to 2.5 each time, with some slight variation to make certain examples fit better. Based on this, I would agree with a nightingale being Size -9. Thrushes vary from around 20 g to around 180 g, depending on the species. Ideally the writer didn't use the blue whistling thrush since it's not European. Meanwhile the great thrush is around 140 g, and it's a New World bird. So I would not put thrushes at Size -6 since that would only apply to some non-European ones. So for the European ones I would agree with you about Size -9 to Size -7.
Let's see if this holds up with LoM:
partridge: -5 & about 400 g for the grey partridge - looks good
duck: -3 & about 2 kg with lots of variation - looks good
goose: -2 & 2-4 kg (assuming a European one like a greater white-fronted goose or greylag goose) - on the small end, but could be ok depending on the type
pheasant: -2 & about 1 kg for the common pheasant - I think this should be Size -4, not -3.
heron: -2 & 1-2 kg for the grey heron, purple heron, and bittern (I'm assuming the author categorize egrets separately.) - I think this should be well below Size -2 despite their height and wingspan.
crane: -1 & about 5 kg for the common crane - I think this should be Size -2, not Size -1.
Putting this all together... I notice that many birds are one Size greater than their mass/weight would indicate, as you mention is stated. However, I also see a number of birds placed about two Size categories above where their mass/weight would indicate. My estimate would then be that birds are typically about 1.5 Size categories higher than their mass/weight would indicate, one higher for birds with smaller legs and wingspans and two higher for birds with longer legs and wingspans. This estimate still isn't perfect, but it seems pretty close.
In this particular case, I would just say go with Size -7, smaller than the songbird entry. That's still large enough not to have to deal with the Dwarf Flaw. Or maybe you compromise and go with Size -8 and Small Frame instead of Dwarf as an obligatory Flaw. These options should make the player (you) happy while still not throwing the rules out.