Depression has become a big problem in our society today. It is also a major reason for suicide, especially among teenagers. In the current outbreak of coronavirus disease (COVID-19), the affected countries have recommended social distancing and lockdown measures. Resulting in interpersonal isolation, these measures have raised serious concerns for mental health and depression. Generally, clinical psychologists diagnose depressed people via face-to-face interviews following the clinical depression criteria. However, often patients tend to not consult doctors in their early stages of depression. Nowadays, people are increasingly using social media to express their moods. In this article, we aim to predict depressed users as well as estimate their depression intensity via leveraging social media (Twitter) data, in order to aid in raising an alarm. We model this problem as a supervised learning task. We start with weakly labeling the Twitter data in a self-supervised manner. A rich set of features, including emotional, topical, behavioral, user level, and depression-related -gram features, are extracted to represent each user. Using these features, we train a small long short-term memory (LSTM) network using Swish as an activation function, to predict the depression intensities. We perform extensive experiments to demonstrate the efficacy of our method. We outperform the baseline models for depression intensity estimation by achieving the lowest mean squared error of 1.42 and also outperform the existing state-of-the-art binary classification method by more than 2% of accuracy. We found that the depressed users frequently use negative words such as stress and sad, mostly post during late nights, highly use personal pronouns and sometimes also share personal events.