I've now had another think, with specific focus on the context.
Immediately before our passage, at the end of chapter 76, the Athenians have said:
'Thus we think that other people, if they took over our power, would show clearly whether we practise some moderation; however, in consequence of our very reasonableness, ill repute more than praise has unfairly accrued to us.'
It seems most likely that 77.1 must follow directly on from this, and give an instance of such unfairness: thus γὰρ would = 'for example'.
I'm inclining to take the first καὶ as concessive, and the second one as connective - or, perhaps better, as introducing an explanation of the first clause (ἐλασσούμενοι etc.). On this basis, and adopting a somewhat different interpretation of ἐλασσούμενοι, my latest tentative offering is as follows:
'For example, even though we settle for less than we might in cases against our allies under international agreements, and have instituted hearings of such cases in our own courts under equitable laws, we are regarded as litigious.'
Perhaps the point being made is that, given their power, the Athenians could extort far more than they actually settle for if they chose to set aside, or even distort, due process, whereas in fact they are studiously cultivating justice by having such cases heard in their own courts on an equitable basis.
After 77.1 the Athenians expand the thought: because they are seen to treat their subjects as equals before the law, those subjects feel aggrieved if they lose anything in a legal case; if, however, the Athenians had set aside all considerations of equity from the outset, and had simply operated on a basis of 'might makes right', their subjects would have accepted this, and would not have felt aggrieved as at losing out to an (in legal terms) equal.
With regard to the apparent disconnection between the points cited and the accusation of litigiousness, this is perhaps an instance (of which there are a number) of Thucydides' compressing the train of thought, or even omitting a stage altogether (I recall another one at the end of 4.85, in Brasidas' speech to the Acanthians). Perhaps the 'unpacked' meaning here is: 'Even though we do all this to ensure equity, we are nonetheless still criticised - not, it is true, for exercising arbitrary power, but instead for being litigious.' In other words, the Athenians can't (in their view) win: because they choose to work equitably through the courts, all this does is bring down upon them accusations of litigiousness!
Anyway, that's my latest - and, as always with Thucydides, highly provisional - shot at it.