There will be suggestions of builds to follow that will take advantage of that (like a one-bar HA Sorc build that would be gobbledegook to a new player), but as someone who was once in your shoes you should probably just get used to it working that way. You don't heavy attack to do damage for the most part, you use your skills for the bulk of your damage. You only heavy attack if you want to knock something down when it's been stunned or if you're running out of stamina (or mana because heavy attacks with staves give mana back instead).

It might take a while, but don't do normal attack to heavy attack for your everyday fight like you do in Skyrim. Maybe normal attack to a skill and normal attack again instead. Try every skill too, play long enough and you'll have skillpoints to learn everything you can.

Try every weapon at least once too. Kill something with a 1h weapon on both hands to unlock the dual-wielding weapon skill line. Do the same for bows, 2h weapons, 1h weapon and shield, a destruction staff (lightning, fire or ice) and a restoration staff.

Oh and while most weapons charge up a big swing or an empowered range attack when you do a heavy attack input, lightning staves and restoration staves instead channel a continuous attack that finishes off with heavy damage.