The Chantry all but ruled the fractured city-states of the Marches (that's what they got for not compromising on a centralized government).
This isn't actually true. From what we see of the actions of secular governments in the Marches, the Chantry is not the driving force behind them, nor does it command a particularly outsize amount of support or allegiance.
Consider Viscount Dumar, who came to power through templar intervention in city politics and therefore would be expected to be as much a puppet of the Chantry as anyone. Yet there is no point in DA2 where Dumar's actions are depicted as being ordered by the Chantry, or even particularly in Chantry interests. Even Codex entries about Dumar focus on his role as a negotiator and a balancer rather than claiming him to be a templar or clerical puppet. There is in fact a faction of the Kirkwall clergy that is violently opposed to Dumar, up to and including a murderous attack on his son.
Only when Dumar is dead do the templars of Kirkwall exert obvious power over city government. That in itself is fairly instructive: Meredith only gains control when secular authorities do not exist, and when there is no obvious secular successor waiting in the wings.
Our other major example is Starkhaven. The Vael family, when it ruled, apparently had a tradition of piety. DA2's Codex states that they always sent off one of the children to the Chantry for a clerical or lay career. This is, in and of itself, nothing particularly indicative of Chantry control. Medieval European rulers often stashed extraneous children in monasteries or had them ordained as prelates. In certain circumstances, a noble family might even found a monastery as a personal sinecure, into which a portion of family wealth would be deposited for the monks - mostly members of the family itself - to enjoy. While it's true that family members in the Chantry would certainly expose the family to more Chantry 'influence', that's hardly avoidable as a human in Thedas, and that 'influence' flows both ways.
As with Dumar, there is no actual evidence in the games that the Chantry dictated the affairs of Starkhaven under the Vaels.
One might argue in terms of abstraction. If there is no strong government in the Marches, then it would only make sense for the Chantry to gain in power.
Unfortunately, such an argument would rely on some misidentification. There is no central government in the Marches, but there are powerful
local governments with reasonably wide reach. Kirkwall's city guards are nearly omnipresent, and the government appears to take in a wide array of taxes from various sources. Kirkwall's viscount also apparently has significant control over city property ownership, as he is able to effectively 'gift' the arishok an entire compound in a relatively important part of the city. This is really fairly heady stuff for a medieval civic government to be able to do. It's not clear to me where the Chantry would insert itself into the proceedings in a way that a king or emperor or archon would normally do.
I'd also question the notion that the Chantry is necessarily stronger where secular government is weak. Historical example from human history suggests an alternative: that the Chantry might be much stronger when it is closely connected to an existing powerful central secular government. Late classical and medieval Europe abound with examples: the caesaropapist Roman Empire, the Byzantine-Orthodox hybrid state that developed from the late eighth century onward, the Kingdom of France under the rule of Louis IX. One might suggest that Chantry power in Orlais far outstrips anything it might possess in the Marches, due to the proximity of the Divine, the Divine's relevance as an actor in the Game, and the close relationship between the Chantry and the imperial Orlesian state. Those historical examples also cut both ways. There are some examples of religious authorities supplanting secular ones in medieval Europe, sure. There are also plenty of examples of religious authorities failing to do so, even when there is a vast secular power vacuum to exploit. (The history of Germany from the late thirteenth century onward is instructive here.)
Obviously the Chantry is a huge part of the events of
Dragon Age II, and in various forms it plays a highly important role in the final cataclysm at the end of Act III. But I wouldn't jump from that to claiming that the Chantry in the Marches "all but rules". That seems to me to be taking our limited evidence entirely too far.