One of the most common uses of the diminutive in Portuguese as it is spoken in these parts is to excuse or mollify something that might be seen as illegitimate or a nuisance, but which the speaker imbues with positive feeling. The classic example is the ‘jeitinho’, bending the rules, which is the evil twin of sclerotic Brazilian bureaucracy: each exists to thwart the other. That deserves its own post.
Some examples, with glosses:
musiquinha My music may annoy you, but I like it
cervejinha One too many
dinheirinho Come on, it’s not that expensive
comprinhas Shopping spree
cachorrinho It may crap on the pavement, but it’s so sweet
espera só um pouquinho Wait here for the present (with apologies to Laurie Lee)
amiguinhos “just friends”
saidinha Just popping out for a minute
As the last example shows, there are ways of doing this sort of thing in English, as no doubt in all languages (pace Whorf); but my guess is this style is particularly common in just Spanish, Portuguese and Italian (maybe Roumanian) — southern Romance, let’s say.