I'm a healthy weight for my height and my Background insulin is still working okay as i set alarms to wake up last night at 2am and 4am and my results were..
you dont say what basal amount you take or when you take it or even if you split it!
your basal might be ok in the early hours but what is it like for the daytime? has it run out? if so your bolus shots will be fighting your meals and your liver output at the same time.
i would suggest you look at testing your basal level during the day.
i have read gary scheiner 'think like a pancreas' and john walsh's 'using insulin' both very good books that explain in depth how to test and adjust insulin to get the best results.
have a look , you might be surprised.
please bear in mind i am a lowly t2 on b/b so not fully familiar with the trials and tribulations of t1!