They are spindly as a design choice that is an evolution from their previous models. Just like the Cylons of old were clunky, heavily armed and very close to indestructible, so were their Basestars. The original basestars had point defense weapons as well as long range armaments, small contingents of Raiders, and were tankier than the average Battlestar, but the design was very similar, similar in design to our battleships. As they evolved as a biomechanical species, their war machines advanced as well.
Instead of using raw mechanical parts, Cylons switched to the biomechanical plating so the stars can self heal, which we see in the Rebooted series episode Guess What's Coming to Dinner? and also comes into play in the last season. The Original Series Base stars only had certain weapons on certain halves of the ship, providing a vulnerability that the Colonials could exploit (seen in the Hand of God episode of the Original Series).
The updated basestar is more like an American aircraft carrier - Instead of having different batteries of weapons, the New Basestars have Raiders acting as both offense and defense, supplemented with various types of missiles to engage capital ships. The current design allows for larger amounts of Raiders (usually over 400, according to the wiki) that can launch in any direction, and also allows them to shoot missiles in any direction. Looking like a starfish may be a wink-nudge design decision because the 'arms' can grow back. More in-universe, the design may also be desire to make the design aerodynamic, as they do show the basestars able to switch to a Y formation to perform atmospheric flight in Razor.